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