Solve the absolute value inequality. 8&lt;|7−3x|

Question

Solve the absolute value inequality. 8&amp;lt;|7−3x|

avortarF · Accepted Answer

Step 1
First isolate the absolute value expression to the left side of inequality to solve the inequality. Remove the absolute bars by setting a compound inequality. Then solve the inequalities to obtain the solution.
Step 2
The solution to the inequality $8 < | 7 - 3 x |$ can be found as follows.
First isolate the absolute expression by changing the sides as $| 7 - 3 x | > 8$ .
Now apply absolute rule: if $| u | > a$ . then $u < - a o r u > a$ to remove the absolute bars and solve the two inequalities.
$| 7 - 3 x | > 8$ then
$7 - 3 x < - 8$ or $7 - 3 x > 8$
$3 x > 15 o r 3 x < - 1$
$x > 5$ or $x < - \frac{1}{3}$
Hence, the solution to the absolute value inequality $8 < | 7 - 3 x |$ is $x < - \frac{1}{3}$ or $x > 5.$

Solve the absolute value inequality.8<|7-3x|

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