Solve and Graph Linear Inequalities

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Pre-Calculus › Solve and Graph Linear Inequalities

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Solve and graph:

$-6 \le 6x + 3 \le 21$

$-\frac{9}{6} \leq x \leq 3$

CORRECT

$x \leq 21$

0

$x \geq 6$

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$x \geq 9$

0

$x \geq \frac{21}{6}$

0

Explanation

Write $-6 \le 6x + 3 \le 21$ as two simple inequalities:

$-6 \leq 6x + 3$ $6x + 3 \leq 21$

Solve the inequalities:

$-3 - 6 \leq 6x$ $6x \leq 21 - 3$

$-9 \leq 6x$ $6x \leq 18$

$-\frac{9}{6} \leq x$ $x \leq 3$

Write the final solution as a single compound inequality:

$-\frac{9}{6} \leq x \leq 3$

For interval notation:

$[-\frac{9}{6}, 3] = [-1 \frac{3}{6}, 3]$

Now graph:

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