QuestionSolve for $x$ : $7(x+4)+2=-4(x-11)-8$

Studdy Solution

STEP 1

Assumptions1. The equation to solve is $7(x+4)+=-4(x-11)-8$ . We are solving for the variable $x$
3. The equation is linear, meaning there is only one solution for $x$

STEP 2

First, we need to distribute the numbers outside the parentheses to the terms inside the parentheses.
$7(x+4)+2=-4(x-11)-8$ becomes $7x+28+2=-4x+44-8$

STEP 3

Now, simplify the equation by combining like terms on each side.
$7x+30=-x+36$

STEP 4

Next, we want to isolate $x$ by getting all terms with $x$ on one side of the equation and the constants on the other side. Start by adding $4x$ to both sides of the equation.
$7x+4x+30=-4x+4x+36$

STEP 5

implify the equation by combining like terms.
$11x+30=36$

STEP 6

Continue to isolate $x$ by subtracting $30$ from both sides of the equation.
$11x+30-30=36-30$

STEP 7

implify the equation by combining like terms.
$11x=6$

STEP 8

Finally, solve for $x$ by dividing both sides of the equation by $11$ .
$x=\frac{6}{11}$ So, the solution to the equation is $x=\frac{6}{11}$ .

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