QuestionSolve the linear equation: $6(3x - 3) = -19(3 - x)$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is a linear equation. . The equation is in the form of $ax + b = cx + d$ .
3. We need to solve for the variable $x$ .

STEP 2

First, we need to distribute the numbers outside the parentheses on both sides of the equation.
$6(x -) = -19( - x)$

STEP 3

istribute the6 on the left side of the equation.
$6 \cdot3x -6 \cdot3 = -19(3 - x)$

STEP 4

implify the left side of the equation.
$18x -18 = -19(3 - x)$

STEP 5

istribute the -19 on the right side of the equation.
$18x -18 = -19 \cdot3 +19 \cdot x$

STEP 6

implify the right side of the equation.
$18x -18 = -57 +19x$

STEP 7

Now, we need to isolate the variable $x$ on one side of the equation. We can do this by subtracting $18x$ from both sides of the equation.
$18x -18x -18 = -57 +19x -18x$

STEP 8

implify both sides of the equation.
$-18 = -57 + x$

STEP 9

To isolate $x$ , add57 to both sides of the equation.
$-18 +57 = -57 + x +57$

STEP 10

implify both sides of the equation to find the value of $x$ .
$x =39$ So, the solution to the equation $6(3x -3) = -19(3 - x)$ is $x =39$ .

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