Solve −3x + 1 ≥ 12
Linear inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | x ≤ −11/3 |
| Interval notation | (−∞, −11/3] |
Step-by-step solution
4 steps-
1 Given- 3 x + 1 \ge 12
Solve for x.
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2 Subtract 1 from both sides
Like an equation, an inequality stays true when the same amount is added to or subtracted from both sides. Only multiplying or dividing by a negative number needs extra care: it reverses the sign.
- 3 x \ge 11Move the constant terms to the right.
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3 Divide both sides by -3 and reverse the inequality sign
Multiplying or dividing by a negative number reverses the order of numbers: 2 < 3, but −2 > −3. So the inequality sign has to be turned around to stay true.
x \le - \frac{11}{3}Multiplying or dividing both sides by a negative number reverses the inequality.
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4 Solutionx \le - \frac{11}{3}\qquad \left( -\infty, - \frac{11}{3} \right]
Check with test values
| x | Left side | Right side | Holds? |
|---|---|---|---|
| −4 | 13 | 12 | ✓ true |
| −3 | 10 | 12 | ✗ false |
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