Dolly Robinson

2020-10-31

Solve absolute value inequality : $|3x-8|>7$

tabuordy

Step 1
the given absolute value inequality is:
$|3x-8|>7$
we have to solve the given absolute value inequality.
Step 2
the given absolute value inequality is $|3x-8|>7$
$|3x-8|>7$
as we know that if $|x|>a$ then $x\in \left(-\mathrm{\infty },-a\right)\cup \left(a,\mathrm{\infty }\right)$
that implies if $|x|>a$ then $x<-a\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}x>a$
therefore,
if $|3x-8|>7$ then
$3x-8<-7\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}3x-8>7$
Therefore,
for $3x-8<-7$
$3x-8+8<-7+8$
$3x<1$
$x<\frac{1}{3}$
Step 3
for $3x-8>7$
$3x-8+8>7+8$
$3x>15$
$x>\frac{15}{3}$
$x>5$
therefore, if $|3x-8|>7$ then $x<13\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}x>5$
therefore the solution of the given absolute value inequality $|3x-8|>7$ is $x<13\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}x>5$
therefore the solution of the given absolute value inequality $|3x-8|>7$ in interval notation is
$x\in \left(-\mathrm{\infty },\frac{1}{3}\right)\cup \left(5,\mathrm{\infty }\right)$

Jeffrey Jordon

Answer is given below (on video)

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