Absolute Value Inequalities

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College Algebra › Absolute Value Inequalities

Questions 1 - 2

1

Solve the inequality:

$8+\left | 4x-7\right |\geq17$

$x\geq4:or: x\leq-\frac{1}{2}$

$x\leq 4:or: x\geq -\frac{1}{2}$

$x\geq-2$

$x\geq2:or: x\leq\frac{3}{4}$

$x\leq-\frac{1}{}5$

Explanation

To solve for first isolate the absolute value portion on one side of the equation and all other constants on the other side.

$8+\left | 4x-7\right |\geq17$

$\left | 4x-7\right |\geq9$

Since absolute values can come from either negative or positive values, two equations need to be set up and solved for.

$4x-7\geq9;or;4x-7\leq-9$

$4x\geq16;or;4x-7\leq-2$

$x\geq4:or: x\leq-\frac{1}{2}$

2

Solve:

$x>\frac{14}{3}$

$x<\frac{14}{3}$

$x<-\frac{14}{3}$

Explanation

Add on both sides.

Add 8 on both sides.

Divide by two on both sides.

$\frac{2x}{2}<\frac{28}{2}$

The answer is:

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