Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 19, 2024

Solve the equation $-2(x+11)=-8$ to find the value of $x$ .

STEP 1

Assumptions
1. We are given the equation $-2(x+11)=-8$ .
2. We need to solve for $x$ .

STEP 2

First, we need to distribute the $-2$ across the terms inside the parentheses.
$-2(x+11) = -2 \cdot x + (-2) \cdot 11$

STEP 3

Perform the multiplication to simplify the left side of the equation.
$-2 \cdot x + (-2) \cdot 11 = -2x - 22$

STEP 4

Now, rewrite the equation with the simplified left side.
$-2x - 22 = -8$

STEP 5

To isolate $x$ , we need to get rid of the $-22$ on the left side. We do this by adding $22$ to both sides of the equation.
$-2x - 22 + 22 = -8 + 22$

STEP 6

Simplify both sides of the equation.
$-2x = 14$

STEP 7

Now, to solve for $x$ , we need to divide both sides of the equation by $-2$ to isolate $x$ .
$\frac{-2x}{-2} = \frac{14}{-2}$

STEP 8

Perform the division to find the value of $x$ .
$x = -7$
The solution to the equation $-2(x+11)=-8$ is $x = -7$ .

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