Solve absolute value inequality : |3x−8|&gt;7

Question

Solve absolute value inequality : |3x−8|&amp;gt;7

tabuordy · Accepted Answer

Step 1
the given absolute value inequality is:
$| 3 x - 8 | > 7$
we have to solve the given absolute value inequality.
Step 2
the given absolute value inequality is $| 3 x - 8 | > 7$
$| 3 x - 8 | > 7$
as we know that if $| x | > a$ then $x \in (- \infty, - a) \cup (a, \infty)$
that implies if $| x | > a$ then $x < - a or x > a$
therefore,
if $| 3 x - 8 | > 7$ then
$3 x - 8 < - 7 or 3 x - 8 > 7$
Therefore,
for $3 x - 8 < - 7$
$3 x - 8 + 8 < - 7 + 8$
$3 x < 1$
$x < \frac{1}{3}$
Step 3
for $3 x - 8 > 7$
$3 x - 8 + 8 > 7 + 8$
$3 x > 15$
$x > \frac{15}{3}$
$x > 5$
therefore, if $| 3 x - 8 | > 7$ then $x < 13 or x > 5$
therefore the solution of the given absolute value inequality $| 3 x - 8 | > 7$ is $x < 13 or x > 5$
therefore the solution of the given absolute value inequality $| 3 x - 8 | > 7$ in interval notation is
$x \in (- \infty, \frac{1}{3}) \cup (5, \infty)$

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Solve absolute value inequality : abs(3x - 8) > 7

Answered question

Answer & Explanation

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