Solve 4x + 6 > −4
Linear inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | x > −5/2 |
| Interval notation | (−5/2, ∞) |
Step-by-step solution
4 steps-
1 Given4 x + 6 > -4
Solve for x.
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2 Subtract 6 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.
4 x > -10Move the constant terms to the right.
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3 Divide both sides by 4x > - \frac{5}{2}
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4 Solutionx > - \frac{5}{2}\qquad \left( - \frac{5}{2}, \infty \right)
Check with test values
| x | Left side | Right side | Holds? |
|---|---|---|---|
| −2 | −2 | −4 | ✓ true |
| −3 | −6 | −4 | ✗ false |
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