QuestionSolve for x: 4(2x - 4) - 5x + 4 = -30

Studdy Solution

STEP 1

Assumptions1. We are solving for the variable $x$ in the equation $4(x-4)-5x+4=-30$ . . The equation is a linear equation, meaning it can be solved by isolating the variable $x$ on one side of the equation.

STEP 2

First, we need to distribute the $4$ in the term $4(2x-4)$ .
$4(2x-4) =4 \cdot2x -4 \cdot4$

STEP 3

Calculate the distributed values.
$(2x-) =8x -16$

STEP 4

Now, replace the term $4(2x-4)$ in the original equation with the result from the previous step.
$8x -16 -x +4 = -30$

STEP 5

Next, we need to combine like terms on the left side of the equation.
$8x -5x -16 +4 = -30$

STEP 6

Calculate the combined values.
$3x -12 = -30$

STEP 7

To isolate $x$ , we need to first get rid of the $-12$ on the left side of the equation. We can do this by adding $12$ to both sides of the equation.
$3x -12 +12 = -30 +12$

STEP 8

Calculate the new values.
$3x = -18$

STEP 9

Finally, to solve for $x$ , we need to divide both sides of the equation by $3$ .
$\frac{3x}{3} = \frac{-18}{3}$

STEP 10

Calculate the value of $x$ .
$x = -6$ So, the solution to the equation $4(2x-4)-5x+4=-30$ is $x = -6$ .

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