QuestionSolve for $x$ : $2|3 x-4|+15=43$

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, and is always positive or zero. . The equation given is $|3x-4|+15=43$ .

STEP 2

First, we isolate the absolute value term by subtracting15 from both sides of the equation.
$2|x-4|+15-15=43-15$

STEP 3

implify the equation.
$2|3x-|=28$

STEP 4

Next, we divide both sides of the equation by2 to isolate the absolute value term.
$\frac{2|3x-4|}{2}=\frac{28}{2}$

STEP 5

implify the equation.
$|3x-4|=14$

STEP 6

Now, we can remove the absolute value by setting up two equations, one for the positive value and one for the negative value.
$3x-4=14 \quad and \quad3x-4=-14$

STEP 7

olve the first equation by adding4 to both sides.
$3x-4+4=14+4$

STEP 8

implify the equation.
$3x=18$

STEP 9

Divide both sides by3 to solve for x.
$\frac{3x}{3}=\frac{18}{3}$

STEP 10

implify the equation.
$x=6$

STEP 11

Now, solve the second equation by adding4 to both sides.
$3x-4+4=-14+4$

STEP 12

implify the equation.
$x=-10$

STEP 13

Divide both sides by3 to solve for x.
$\frac{3x}{3}=\frac{-10}{3}$

STEP 14

implify the equation.
$x=-\frac{10}{3}$ The solutions to the equation are $x=6$ and $x=-\frac{10}{3}$ .

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