Solve −5x − 1 ≤ 7
Linear inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | x ≥ −8/5 |
| Interval notation | [−8/5, ∞) |
Step-by-step solution
4 steps-
1 Given- 5 x - 1 \le 7
Solve for x.
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2 Add 1 to 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.
- 5 x \le 8Move the constant terms to the right.
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3 Divide both sides by -5 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 \ge - \frac{8}{5}Multiplying or dividing both sides by a negative number reverses the inequality.
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4 Solutionx \ge - \frac{8}{5}\qquad \left[ - \frac{8}{5}, \infty \right)
Check with test values
| x | Left side | Right side | Holds? |
|---|---|---|---|
| −1 | 4 | 7 | ✓ true |
| −2 | 9 | 7 | ✗ false |
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