Algebra worked examples
Classic textbook problems, each worked out line by line by the Step-by-Step Algebra Solver: every move named, every answer checked.
Linear equations
- Solve 2x + 5 = 11
- Solve 3(x − 2) = 2x + 7
- Solve 5x − 3 = 2x + 9
- Solve 4 − 2(x + 1) = 3x − 8
- Solve (x + 1)/3 = (x − 2)/2
- Solve 0.5x + 1.2 = 3.7
- Solve 4x + 1 = −7
- Solve 6x + 1 = 3x + 19
- Solve 2(x − 9) = −2
- Solve (x + 7)/4 = 8
- Solve 4x − 3(x − 2) = 5
- Solve 6 − 7x = −29
- Solve x/2 + x/4 = 3
- Solve 2.5x + 4 = 16.5
- Solve 6x + 3 = 57
- Solve 7x + 3 = 5x + 1
- Solve 5(x + 7) = 45
- Solve (x − 2)/2 = 8
- Solve 4x − 2(x − 2) = 14
- Solve 1 − 4x = −19
- Solve x/3 + x/6 = 9
- Solve 1.5x + 2.5 = 10
- Solve 3x + 2 = 11
- Solve 9x − 5 = 5x − 29
- Solve 4(x + 4) = 52
- Solve (x + 6)/5 = 5
- Solve 5x − 2(x − 2) = 1
- Solve 7 − 6x = −41
- Solve x/3 + x/6 = −3
- Solve 0.4x + 1.2 = 0.4
- Solve 4x − 9 = −5
- Solve 5x + 7 = 4x + 9
- Solve 5(x + 6) = 15
- Solve (x + 6)/2 = 3
- Solve 2x − 3(x − 2) = 3
- Solve 6 − 7x = 6
- Solve x/3 + x/6 = 4
- Solve 0.25x + 0.75 = 1.75
- Solve 6x + 6 = −12
- Solve 3x + 8 = x + 16
- Solve 2(x − 2) = −4
- Solve (x − 1)/4 = 6
- Solve 7x − 3(x − 2) = 26
- Solve 9 − 9x = −72
- Solve x/2 + x/5 = 7
- Solve 1.5x + 2.5 = 7
- Solve 6x − 3 = −21
- Solve 2x − 2 = x − 5
- Solve 2(x + 1) = 14
- Solve (x + 4)/4 = 9
- Solve 7x − 3(x − 2) = 18
- Solve 3 − 2x = −7
- Solve x/3 + x/4 = 14
- Solve 0.2x + 1.4 = 1
- Solve 3x − 6 = 0
- Solve 6x − 4 = 4x + 12
- Solve 3(x − 8) = 3
- Solve (x − 5)/3 = −1
- Solve 7x − 3(x − 2) = 6
- Solve −9 − 5x = −39
- Solve x/3 + x/6 = −2
- Solve 0.5x + 1.5 = 4
Quadratic equations
- Solve x² − 5x + 6 = 0
- Solve x² + 5x + 6 = 0
- Solve x² − 4x − 5 = 0
- Solve 2x² + 3x − 2 = 0
- Solve x² − 9 = 0
- Solve x² + 4x + 4 = 0
- Solve x² + 6x − 7 = 0 by completing the square
- Solve x² − 2x − 1 = 0
- Solve x² + 2x + 5 = 0
- Solve (x − 3)² = 16
- Solve x² − 8x + 7 = 0
- Solve 6x² − 30x + 36 = 0
- Solve x² − 144 = 0
- Solve x² = 4
- Solve x² + 2x + 1 = 0
- Solve x² + 6x − 3 = 0 by completing the square
- Solve x² + x − 1 = 0
- Solve 2x² + 6x + 4 = 0 with the quadratic formula
- Solve 5x² = 45
- Solve (x + 3)² = 25
- Solve x(x − 1) = 12
- Solve x² + 1 = 0
- Solve x² + 7x = 0
- Solve x² − 4 = 3x
- Solve x² − 3x − 28 = 0
- Solve 3x² + 12x + 12 = 0
- Solve x² − 81 = 0
- Solve x² = 9
- Solve x² + 8x + 16 = 0
- Solve x² + 4x − 1 = 0 by completing the square
- Solve x² + 7x + 3 = 0
- Solve 2x² + 2x − 4 = 0 with the quadratic formula
- Solve x² = 5
- Solve (x + 1)² = 36
- Solve x(x + 4) = 10
- Solve x² + 4 = 0
- Solve x² − 4x = 0
- Solve 2x² = 8x
- Solve x² − 3x − 10 = 0
- Solve 4x² + 20x + 16 = 0
- Solve x² − 49 = 0
- Solve x² = 144
- Solve x² − 6x + 9 = 0
- Solve x² + 10x + 7 = 0 by completing the square
- Solve x² + 6x + 4 = 0
- Solve 2x² + 7x + 3 = 0 with the quadratic formula
- Solve 2x² = 50
- Solve (x − 2)² = 9
- Solve x(x + 3) = 10
- Solve x² + 9 = 0
- Solve x² − 6x = 0
- Solve x² + 3x = 10
- Solve x² − 2x + 1 = 0
- Solve 10x² + 7x + 1 = 0
- Solve x² − 121 = 0
- Solve x² = 121
- Solve x² + 6x + 9 = 0
- Solve x² + 2x − 5 = 0 by completing the square
- Solve x² + 2x − 2 = 0
- Solve 2x² + 2x − 2 = 0 with the quadratic formula
- Solve 4x² = 100
- Solve (x + 4)² = 9
- Solve x(x + 5) = 15
- Solve x² + 16 = 0
- Solve x² + 3x = 0
- Solve x² = 2x + 15
- Solve x² + 12x + 32 = 0
- Solve 6x² − 21x + 18 = 0
- Solve x² − 16 = 0
- Solve x² = 100
Polynomial equations
- Solve x³ − 6x² + 11x − 6 = 0
- Solve x³ = 8
- Solve x⁴ − 5x² + 4 = 0
- Solve x³ − 19x + 30 = 0
- Solve x⁴ = 1
- Solve x³ − 4x = 0
- Solve x⁴ − 25x² + 144 = 0
- Solve x³ + 2x² − x − 2 = 0
- Solve x³ + 5x² − 4x − 20 = 0
- Solve x³ = 27
- Solve x³ − x = 0
- Solve x⁴ − 13x² + 36 = 0
- Solve x³ + 4x² − x − 4 = 0
- Solve x³ − 13x − 12 = 0
- Solve x³ = 125
- Solve x³ − 16x = 0
- Solve x⁴ − 17x² + 16 = 0
- Solve x³ + x² − 4x − 4 = 0
- Solve x³ − 2x² − x + 2 = 0
- Solve x³ = 1
- Solve x³ − 9x = 0
- Solve x⁴ − 29x² + 100 = 0
- Solve x³ + 2x² − 3x − 6 = 0
- Solve x³ + 4x² − 25x − 100 = 0
- Solve x³ = 64
- Solve x³ − 25x = 0
- Solve x⁴ − 10x² + 9 = 0
- Solve x³ + 3x² − 2x − 6 = 0
- Solve x³ − 3x² − 6x + 8 = 0
- Solve x⁴ = 625
- Solve x³ − 2x² − 19x + 20 = 0
- Solve x⁴ = 256
- Solve x³ − 4x² − x + 4 = 0
- Solve x⁴ = 16
- Solve x³ − 5x² − 16x + 80 = 0
- Solve x⁴ = 81
- Solve x³ + 2x² − 23x − 60 = 0
Radical and rational equations
- Solve √(x + 3) = x − 3
- Solve √(2x + 1) = 3
- Solve 1/x + 1/2 = 3/4
- Solve (x + 1)/(x − 2) = 3
- Solve √(2x + 15) = 3
- Solve √(x − 2) = x − 2
- Solve 12/x = 4
- Solve (x + 1)/(x − 3) = 5
- Solve 1/x + 1/4 = 3/4
- Solve x/(x − 3) = 4
- Solve 3/(x − 1) = 1/(x + 2)
- Solve x + 6/x = 5
- Solve √(4x − 15) = 1
- Solve √(x + 41) = x − 1
- Solve 15/x = 3
- Solve (x + 5)/(x − 2) = 2
- Solve 1/x + 1/3 = 5/6
- Solve x/(x − 4) = 2
- Solve 2/(x − 1) = 3/(x + 2)
- Solve x + 3/x = 4
- Solve √(4x + 29) = 5
- Solve √(x + 39) = x − 3
- Solve 6/x = 2
- Solve (x + 3)/(x − 2) = 2
- Solve 1/x + 1/2 = 1/2
- Solve x/(x − 5) = 6
- Solve 4/(x − 1) = 3/(x + 2)
- Solve x + 4/x = 5
- Solve √(2x + 36) = 6
- Solve √(x + 1) = x − 1
- Solve 8/x = 4
- Solve (x + 2)/(x − 1) = 4
- Solve 1/x + 1/6 = 1/2
- Solve x/(x − 2) = 3
- Solve 2/(x − 1) = 5/(x + 2)
- Solve x + 8/x = 6
- Solve √(3x + 12) = 3
- Solve √(x + 30) = x
- Solve 10/x = 2
- Solve (x + 4)/(x − 1) = 3
- Solve 1/x + 1/3 = 2/3
- Solve x/(x − 1) = 2
- Solve 1/(x − 1) = 4/(x + 2)
- Solve x + 12/x = 7
- Solve √(3x + 43) = 7
- Solve √(x + 20) = x
- Solve 18/x = 3
- Solve 1/x + 1/5 = 7/10
Absolute value equations
- Solve |2x − 3| = 5
- Solve |3x − 5| = 7
- Solve 2|x + 2| − 6 = 18
- Solve |x − 4| + 2 = 8
- Solve |4x − 3| = 10
- Solve 3|x + 5| − 3 = 9
- Solve |x − 3| + 5 = 16
- Solve |3x + 4| = 4
- Solve 2|x − 9| − 1 = 17
- Solve |x − 5| + 5 = 13
- Solve |2x − 9| = 7
- Solve 2|x − 7| − 4 = 8
- Solve |x − 9| + 5 = 13
- Solve |x + 1| = 12
- Solve 2|x + 6| − 4 = 10
- Solve |x − 9| + 1 = 15
- Solve |4x − 5| = 8
- Solve 3|x − 6| − 2 = 4
- Solve |x + 6| + 3 = 18
- Solve |x + 2| = 12
- Solve 2|x − 2| − 4 = 4
- Solve |x − 2| + 5 = 10
- Solve |2x + 4| = 3
- Solve 3|x − 5| − 1 = 20
- Solve |x − 6| + 5 = 8
- Solve |3x + 6| = 12
- Solve 3|x − 3| − 5 = 25
- Solve |x − 1| + 3 = 14
- Solve |x − 2| = 4
Exponential and logarithmic equations
- Solve 2^x = 32
- Solve 3^(x + 1) = 81
- Solve e^x = 5
- Solve log(x) + log(x − 3) = 1
- Solve ln(x) = 2
- Solve 3^x = 9
- Solve 4^(x + 1) = 64
- Solve 5^(2x − 1) = 3125
- Solve 8^x = 64
- Solve 5^x = 7
- Solve e^(2x) = 10
- Solve ln(x) = 10
- Solve log(x) = 1
- Solve log2(x) = 4
- Solve 3 · 2^x = 12
- Solve log(x) + log(x − 9) = 1
- Solve e^(x − 1) = 7
- Solve 2^x = 16
- Solve 3^(x + 1) = 27
- Solve 2^(2x − 1) = 8
- Solve 9^x = 81
- Solve 2^x = 5
- Solve e^x = 4
- Solve ln(x) = 3
- Solve log(x) = 3
- Solve log2(x) = 2
- Solve 3 · 2^x = 24
- Solve log(x) + log(x − 21) = 2
- Solve 2e^x − 3 = 5
- Solve 3^x = 27
- Solve 2^(x + 1) = 32
- Solve 5^(2x − 1) = 125
- Solve 27^x = 729
- Solve 2^x = 12
- Solve e^x = 10
- Solve ln(x) = 4
- Solve log(x) = 2
- Solve log2(x) = 3
- Solve 3 · 2^x = 3072
- Solve log2(x) + log2(x − 4) = 5
- Solve log_5(x) = 2
- Solve 5^x = 25
- Solve 2^(x + 1) = 16
- Solve 10^(2x − 1) = 100000
- Solve 25^x = 125
- Solve 10^x = 3
- Solve e^x = 2
- Solve ln(x) = 5
- Solve log(x) = 4
- Solve log2(x) = 10
- Solve 3 · 2^x = 48
Trigonometric equations
- Solve sin(x) = 1/2
- Solve 2cos(x) + 1 = 0
- Solve tan(x) = 1 in degrees
- Solve sin(x) = 1
- Solve sin(x) = 1/2 in degrees
- Solve cos(x) = −√(3)/2
- Solve cos(x) = −√(3)/2 in degrees
- Solve tan(x) = −1 in degrees
- Solve sin(3x) = 1
- Solve sin(x) = −1/2
- Solve sin(x) = −√(3)/2 in degrees
- Solve cos(x) = √(3)/2
- Solve cos(x) = −1 in degrees
- Solve tan(x) = −√(3) in degrees
- Solve 4sin(x)² = 3
- Solve sin(x) = 0
- Solve sin(x) = √(2)/2 in degrees
- Solve cos(x) = 0
- Solve cos(x) = −1/2 in degrees
- Solve tan(x) = −√(3)
- Solve 2cos(x) − 1 = 0
- Solve sin(x) = −√(3)/2
- Solve sin(x) = 1 in degrees
- Solve cos(x) = 1
- Solve cos(x) = 1/2 in degrees
- Solve tan(x) = √(3)/3
- Solve tan(x)² = 3
- Solve sin(x) = −1
- Solve sin(x) = −1/2 in degrees
- Solve cos(x) = √(2)/2
- Solve cos(x) = −√(2)/2 in degrees
- Solve tan(x) = √(3) in degrees
- Solve sin(x)² = 1/4
- Solve sin(x) = −√(2)/2
- Solve sin(x) = 0 in degrees
- Solve cos(x) = −1
- Solve cos(x) = √(2)/2 in degrees
Inequalities
- Solve 3x − 2 > 7
- Solve −2x + 5 ≥ 1
- Solve −3 < 2x + 1 ≤ 5
- Solve x² − 4 > 0
- Solve |x − 2| < 3
- Solve (x − 1)/(x + 2) ≥ 0
- Solve 5x − 1 ≥ −1
- Solve −2x + 5 ≤ 7
- Solve −4 < 3x + 5 ≤ 2
- Solve x² + 10x + 24 ≥ 0
- Solve (x + 1)/(x − 2) < 0
- Solve |2x − 5| ≥ 3
- Solve 2x − 9 ≥ −9
- Solve −5x − 1 ≤ 7
- Solve 0 < 2x + 3 ≤ 7
- Solve x² − 4x − 12 ≤ 0
- Solve (x + 4)/(x + 1) > 0
- Solve |2x + 2| ≥ 8
- Solve 2x − 1 ≥ 6
- Solve −3x + 1 ≥ 12
- Solve −1 < 2x + 3 ≤ 7
- Solve x² + 17x + 72 ≥ 0
- Solve (x − 4)/(x − 2) < 0
- Solve |2x + 0| < 2
- Solve 4x − 8 ≤ 6
- Solve −5x − 6 ≥ 9
- Solve −5 < 2x − 1 ≤ 9
- Solve x² + 2x − 3 ≤ 0
- Solve (x + 5)/(x + 3) < 0
- Solve |2x + 3| < 3
- Solve 4x + 6 > −4
- Solve −4x + 2 > 13
- Solve −4 < 2x + 5 ≤ 2
- Solve x² − 10x + 9 ≥ 0
- Solve (x − 1)/(x − 5) < 0
- Solve |2x + 2| ≥ 3
- Solve 4x − 6 ≤ 2
- Solve −5x − 5 < −4
- Solve 2 < 2x + 5 ≤ 8
- Solve x² + 3x − 4 < 0
- Solve (x + 2)/(x + 1) > 0
- Solve |x − 6| ≤ 3
- Solve 5x − 3 < 2
- Solve −3x − 1 ≥ −8
- Solve −8 < 2x + 4 ≤ 0
- Solve x² − x − 56 < 0
- Solve (x − 4)/(x + 3) < 0
- Solve |2x + 0| ≥ 3
- Solve 3x + 1 < 7
- Solve −5x − 8 ≤ 3
- Solve −5 < 2x − 4 ≤ 4
- Solve x² + 5x − 6 > 0
- Solve (x + 5)/(x − 3) > 0
- Solve |2x − 6| < 3
- Solve 3x + 2 < −4
- Solve −5x − 3 < −7
Systems of equations and lines
- Solve x + y = 5, x − y = 1
- Solve 2x + 3y = 12, 4x − y = 10
- Solve x² + y² = 25, x + y = 7
- Solve 2x + 3y = 6
- Solve x + 2y = 10, −5x − y = 13
- Solve −x − y = −7, −3x + 3y = −3 by elimination
- Solve −x − y = −5, 3x + 5y = 29 with Cramer’s rule
- Solve −2x + 3y = 12, 4x − 4y = −12 by substitution
- Solve 2x + y + z = 3, −2x − y − z = −3, 3x + y + z = 4
- Solve x² + y² = 13, x + y = 5
- Solve y = x², y = 2x
- Solve x + 3y = 9
- Solve −3x − 4y = −31, 4x + 4y = 36
- Solve 5x − 5y = 15, 4x − 3y = 8 by elimination
- Solve 4x − 2y = 0, 3x − 4y = −10 with Cramer’s rule
- Solve 4x + 3y = 31, 2x + 5y = 33 by substitution
- Solve −x − 2y + 2z = 7, x + y − z = −3, 2x − y + z = 6
- Solve x² + y² = 25, x + y = −1
- Solve x² − y = 1, x + y = 5
- Solve 3x + 2y = 12
- Solve 5x + 3y = 8, −4x − 4y = −16
- Solve 2x − 3y = −28, −x − y = −1 by elimination
- Solve 3x − 2y = −5, −2x + 2y = 2 with Cramer’s rule
- Solve 3x + 2y = −5, 2x − 5y = 3 by substitution
- Solve x + y + 3z = 6, 2x − y + 3z = 15, 3x + 3y + 3z = 6
- Solve x² + y² = 5, x + y = 3
- Solve y = x², y = x + 6
- Solve x − 2y = 4
- Solve 2x − y = 19, x − 5y = 32
- Solve −5x − 4y = 17, 2x + 5y = 0 by elimination
- Solve −3x − 3y = −9, −2x + 4y = −24 with Cramer’s rule
- Solve −5x + y = 11, −x − 3y = −17 by substitution
- Solve 2x + 3y + z = −2, −x + y + 3z = 4, x + 3y + 2z = −1
- Solve x² + y² = 25, x + y = 1
- Solve y = x² − 4, y = 2x − 1
- Solve 2x − y = 3
- Solve x + 5y = −9, −x + 2y = 2
- Solve 3x − 4y = 16, x − 5y = 9 by elimination
- Solve x + y = 1, −5x − y = −25 with Cramer’s rule
- Solve 5x + y = −29, −x − y = 9 by substitution
- Solve x − 2y + z = −1, x + y − 2z = 2, 3x + y − z = 1
- Solve x² + y² = 10, x + y = 4
- Solve y = x², y = x + 2
- Solve 5x + 2y = 10
Expanding, factoring and simplifying
- Expand (x + 3)²
- Expand (2x − 1)(x + 4)
- Factor x² − 5x + 6
- Factor x² − 16
- Simplify (x² − 9)/(x − 3)
- Expand (x + 6)²
- Expand (x − 4)²
- Expand (x + 5)(x − 5)
- Expand (3x + 2)(x − 6)
- Factor x² − 7x − 8
- Factor 4x² − 36
- Factor 2x² − 5x − 3
- Factor 4x² + 8x + 12
- Factor 2x³ − 16
- Expand (x − 2)³
- Simplify (x² + 7x + 6)/(x + 1)
- Expand (x + 7)²
- Expand (x − 2)²
- Expand (x + 7)(x − 7)
- Expand (3x + 5)(2x + 4)
- Factor x² − 5x + 4
- Factor 4x² − 4
- Factor 2x² + 7x + 3
- Factor 3x² + 12x + 9
- Factor x³ + 3x² + 2x + 6
- Expand (2x − 3)²
- Simplify (x² − 4)/(x + 2)
- Expand (x + 4)²
- Expand (x − 8)²
- Expand (x + 1)(x − 1)
- Expand (2x − 5)(3x + 2)
- Factor x² − 15x + 56
- Factor 6x² + x − 2
- Expand (x + 1)³
- Simplify (2x + 4)/(x² − 4)
- Expand (x + 2)²
- Expand (x − 1)²
- Expand (x + 8)(x − 8)
- Expand (x − 4)(2x + 5)
- Factor x² − 5x − 36
- Factor 3x² + 5x + 2
- Expand 3(x + 2)(x − 1)
- Simplify (x² − 1)/(x + 1)
- Expand (x + 5)²
- Expand (x − 6)²
- Expand (x + 6)(x − 6)
- Expand (3x − 1)(x + 2)
- Factor x² + 6x + 8
- Factor 5x² + 13x + 6
- Simplify (x² − 9)/(x + 3)
- Expand (x + 1)²