Question Solve the linear equation $3(9-8x-4x)+8(3x+4)=11$ and select the correct solution.

Studdy Solution

STEP 1

Assumptions
1. The equation to solve is $3(9 - 8x - 4x) + 8(3x + 4) = 11$ .
2. We need to find the value of $x$ that satisfies the equation.

STEP 2

First, distribute the numbers outside the parentheses to the terms inside the parentheses.
$3(9 - 8x - 4x) + 8(3x + 4) = 11$

STEP 3

Multiply $3$ by each term inside the first set of parentheses.
$3 \cdot 9 - 3 \cdot 8x - 3 \cdot 4x + 8(3x + 4) = 11$

STEP 4

Perform the multiplication.
$27 - 24x - 12x + 8(3x + 4) = 11$

STEP 5

Combine the like terms $-24x$ and $-12x$ .
$27 - 36x + 8(3x + 4) = 11$

STEP 6

Now, distribute $8$ to the terms inside the second set of parentheses.
$27 - 36x + 8 \cdot 3x + 8 \cdot 4 = 11$

STEP 7

Perform the multiplication.
$27 - 36x + 24x + 32 = 11$

STEP 8

Combine like terms $27$ and $32$ , and $24x$ and $-36x$ .
$59 - 12x = 11$

STEP 9

To isolate the term containing $x$ , subtract $59$ from both sides of the equation.
$59 - 12x - 59 = 11 - 59$

STEP 10

Simplify both sides of the equation.
$-12x = -48$

STEP 11

To solve for $x$ , divide both sides of the equation by $-12$ .
$\frac{-12x}{-12} = \frac{-48}{-12}$

STEP 12

Calculate the value of $x$ .
$x = 4$
The solution is $x = 4$ , which corresponds to option a.

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