Solve 2x − 1 ≥ 6
Linear inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | x ≥ 7/2 |
| Interval notation | [7/2, ∞) |
Step-by-step solution
4 steps-
1 Given2 x - 1 \ge 6
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.
2 x \ge 7Move the constant terms to the right.
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3 Divide both sides by 2x \ge \frac{7}{2}
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4 Solutionx \ge \frac{7}{2}\qquad \left[ \frac{7}{2}, \infty \right)
Check with test values
| x | Left side | Right side | Holds? |
|---|---|---|---|
| 4 | 7 | 6 | ✓ true |
| 3 | 5 | 6 | ✗ false |
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