Question

10| x – 4| - 3 > 47​

Answer 1

Answer:

x < -1    or    x > 9

Step-by-step explanation:

$10|x-4|-3>47$

Add 3 to both sides.

$10|x-4|-3+3>47+3$

Simplify.

$10|x-4|>50$

Divide both sides by 10.

$\frac{10|x-4|}{10} >\frac{50}{10}$

Simplify.

$|x-4|>5$

Apply absolute value rule: If $|u|>a,a>0$ then $u < -a$ or $u>a$

$x-4$ or $x-4 >5$

$x-4$

Add 4 to both sides.

$x-4+4$

Simplify.

$x$

$x-4>5$

Add 4 to both sides.

$x-4+4>5+4$

Simplify.

$x>9$

Combine the intervals.

$x$ or $x>9$