Solve the Inequality for b -4|6b-8|<=12

$- 4 | 6 b - 8 | \leq 12$

Step 1

Divide each term in $- 4 | 6 b - 8 | \leq 12$ by $- 4$ and simplify.

Divide each term in $- 4 | 6 b - 8 | \leq 12$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 | 6 b - 8 |}{- 4} \geq \frac{12}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 | 6 b - 8 |}{- 4} \geq \frac{12}{- 4}$

Divide $| 6 b - 8 |$ by $1$ .

$| 6 b - 8 | \geq \frac{12}{- 4}$

Simplify the right side.

Divide $12$ by $- 4$ .

$| 6 b - 8 | \geq - 3$

Step 2

Since $| 6 b - 8 |$ is always positive and $- 3$ is negative, $| 6 b - 8 |$ is always greater than $- 3$ so the inequality is always true.

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Solve the Inequality for b -4|6b-8|<=12

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