Question Find the value(s) of $x$ where $5(3x-8)-26=9(x-4)+18$ .

Studdy Solution

STEP 1

Assumptions
1. We have two expressions for $y_1$ and $y_2$ .
2. We need to find the value(s) of $x$ such that $y_1 = y_2$ .

STEP 2

First, write down the given equations for $y_1$ and $y_2$ .
$y_{1} = 5(3x - 8) - 26$ $y_{2} = 9(x - 4) + 18$

STEP 3

Since we are given that $y_1 = y_2$ , set the two expressions equal to each other to find the value(s) of $x$ .
$5(3x - 8) - 26 = 9(x - 4) + 18$

STEP 4

Expand the expressions on both sides of the equation.
$15x - 40 - 26 = 9x - 36 + 18$

STEP 5

Combine like terms on both sides of the equation.
$15x - 66 = 9x - 18$

STEP 6

Subtract $9x$ from both sides to get all the $x$ terms on one side.
$15x - 9x - 66 = -18$

STEP 7

Combine the $x$ terms on the left side of the equation.
$6x - 66 = -18$

STEP 8

Add $66$ to both sides to isolate the term with $x$ .
$6x = 48$

STEP 9

Divide both sides by $6$ to solve for $x$ .
$x = \frac{48}{6}$

STEP 10

Calculate the value of $x$ .
$x = 8$

STEP 11

Since we have found a single value for $x$ , the correct choice is A and the value of $x$ for which $y_1 = y_2$ is $\{8\}$ .
The value(s) of $x$ for which $y_1 = y_2$ is/are $\{8\}$ .

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