QuestionSolve the equation $8(x-3)-2(3-x)=2(x+2)-5(5-x)$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $8(x-3)-(3-x)=(x+)-5(5-x)$ . We need to find the value of $x$ that satisfies this equation

STEP 2

First, we need to distribute the numbers outside the parentheses on both sides of the equation.
On the left side of the equation, distribute $8$ to $(x-)$ and $-2$ to $(-x)$ .
$8(x-)-2(-x) =8x -24 -2(-x)$ On the right side of the equation, distribute $2$ to $(x+2)$ and $-5$ to $(5-x)$ .
$2(x+2)-5(5-x) =2x +4 -5(5-x)$

STEP 3

Continue distributing on both sides of the equation.
On the left side of the equation, distribute $-2$ to $(3-x)$ .
$8x -24 -2(3-x) =8x -24 -6 +2x$ On the right side of the equation, distribute $-5$ to $(5-x)$ .
$2x + -5(5-x) =2x + -25 +5x$

STEP 4

implify both sides of the equation.
On the left side of the equation, combine like terms.
$8x -24 -6 +2x =10x -30$ On the right side of the equation, combine like terms.
$2x +4 -25 +x =7x -21$

STEP 5

Now that we have simplified both sides of the equation, we can set them equal to each other.
$10x -30 =7x -21$

STEP 6

To solve for $x$ , we need to get all terms with $x$ on one side of the equation and the constants on the other side. Subtract $x$ from both sides of the equation.
$10x -x -30 =x -x -21$

STEP 7

implify both sides of the equation.
$3x -30 = -21$

STEP 8

Next, add $30$ to both sides of the equation.
$3x -30 +30 = -21 +30$

STEP 9

implify both sides of the equation.
$3x =9$

STEP 10

Finally, divide both sides of the equation by $3$ to solve for $x$ .
$x =9 /3$

STEP 11

Calculate the value of $x$ .
$x =9 /3 =3$ The solution to the equation is $x=3$ .

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