QuestionSolve the equation: $6(5x - 5) = -31(3 - x)$

Studdy Solution

STEP 1

Assumptions1. The equation is a linear equation. . The equation is in the form of $ax + b = cx + d$ .
3. We are solving for the variable $x$ .

STEP 2

First, we need to distribute the numbers outside the parentheses on both sides of the equation.
$6(5x -5) = -31( - x)$

STEP 3

istribute the6 on the left side of the equation.
$6 \cdot5x -6 \cdot5 = -31(3 - x)$

STEP 4

implify the left side of the equation.
$30x -30 = -31(3 - x)$

STEP 5

istribute the -31 on the right side of the equation.
$30x -30 = -31 \cdot3 +31 \cdot x$

STEP 6

implify the right side of the equation.
$30x -30 = -93 +31x$

STEP 7

Now, we need to isolate the variable $x$ on one side of the equation. Let's start by subtracting $30x$ from both sides of the equation.
$30x -30x -30 = -93 +31x -30x$

STEP 8

implify both sides of the equation.
$-30 = -93 + x$

STEP 9

Next, add93 to both sides of the equation to isolate $x$ .
$-30 +93 = -93 + x +93$

STEP 10

implify both sides of the equation.
$63 = x$ So, the solution to the equation $6(5x -5) = -31(3 - x)$ is $x =63$ .

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