QuestionSolve the equation and check. $x=\square(5+9(x+8)=77-6(4 x+11)$

Studdy Solution

STEP 1

1. The given equation is a linear equation involving one variable, $x$ .
2. The goal is to isolate $x$ and solve for its value.
3. Simplification and distribution of terms will be necessary to solve the equation.

STEP 2

1. Simplify both sides of the equation by distributing terms.
2. Combine like terms on both sides.
3. Move all terms involving $x$ to one side of the equation.
4. Solve for $x$ .
5. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the 9 on the left-hand side and the -6 on the right-hand side.
$5 + 9(x + 8) = 77 - 6(4x + 11)$ $5 + 9x + 72 = 77 - 24x - 66$

STEP 4

Combine the constant terms on both sides of the equation.
$5 + 72 + 9x = 77 - 66 - 24x$ $77 + 9x = 11 - 24x$

STEP 5

Move all terms involving $x$ to one side by adding $24x$ to both sides.
$77 + 9x + 24x = 11$ $77 + 33x = 11$

STEP 6

Subtract 77 from both sides to isolate terms involving $x$ .
$33x = 11 - 77$ $33x = -66$

STEP 7

Solve for $x$ by dividing both sides by 33.
$x = \frac{-66}{33}$ $x = -2$

STEP 8

Check the solution by substituting $x = -2$ back into the original equation.
$5 + 9(-2 + 8) = 77 - 6(4(-2) + 11)$ $5 + 9(6) = 77 - 6(-8 + 11)$ $5 + 54 = 77 - 6(3)$ $59 = 77 - 18$ $59 = 59$ Since both sides of the equation are equal, the solution $x = -2$ is verified.
The solution is $x = -2$ .

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