Solve 5x − 1 ≥ −1
Linear inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | x ≥ 0 |
| Interval notation | [0, ∞) |
Step-by-step solution
4 steps-
1 Given5 x - 1 \ge -1
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 \ge 0Move the constant terms to the right.
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3 Divide both sides by 5x \ge 0
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4 Solutionx \ge 0\qquad \left[ 0, \infty \right)
Check with test values
| x | Left side | Right side | Holds? |
|---|---|---|---|
| 1 | 4 | −1 | ✓ true |
| −1 | −6 | −1 | ✗ false |
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