Solve −2x + 5 ≤ 7
Linear inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | x ≥ −1 |
| Interval notation | [−1, ∞) |
Step-by-step solution
4 steps-
1 Given- 2 x + 5 \le 7
Solve for x.
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2 Subtract 5 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.
- 2 x \le 2Move the constant terms to the right.
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3 Divide both sides by -2 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 -1Multiplying or dividing both sides by a negative number reverses the inequality.
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4 Solutionx \ge -1\qquad \left[ -1, \infty \right)
Check with test values
| x | Left side | Right side | Holds? |
|---|---|---|---|
| 0 | 5 | 7 | ✓ true |
| −2 | 9 | 7 | ✗ false |
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