QuestionSolve for x in the equation: -4(3x + 1) + x - 3 = 15.

Studdy Solution

STEP 1

Assumptions1. We are given the equation $-4(3x+1) + x -3 =15$ . . We need to solve for $x$ .

STEP 2

First, we need to distribute the $-4$ to both terms inside the parentheses.
-4(x+1) + x - = -4 \cdotx -4 \cdot1 + x -

STEP 3

Calculate the multiplication to simplify the equation.
$- \cdot3x - \cdot1 + x -3 = -12x - + x -3$

STEP 4

Combine like terms on the left side of the equation.
$-12x -4 + x -3 = -11x -7$

STEP 5

Now, we have the equation $-11x -7 =15$ . To isolate $x$ , we first need to get rid of the $-7$ on the left side. We can do this by adding $7$ to both sides of the equation.
$-11x -7 +7 =15 +7$

STEP 6

Calculate the addition to simplify the equation.
$-11x =22$

STEP 7

Finally, to solve for $x$ , we need to divide both sides of the equation by $-11$ .
$x = -11x / -11 =22 / -11$

STEP 8

Calculate the division to find the value of $x$ .
$x = -2$ The solution to the equation is $x = -2$ .

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