Question Solve for $u$ in the equation $5(u+3)=8u+24$ . Simplify the solution.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $5(u+3)=8u+24$ .
2. We need to solve for the variable $u$ .

STEP 2

Distribute the 5 on the left-hand side of the equation to both terms inside the parentheses.
$5(u+3) = 5 \cdot u + 5 \cdot 3$

STEP 3

Perform the multiplication.
$5u + 15 = 8u + 24$

STEP 4

We will now isolate the variable $u$ on one side of the equation. Let's move all terms containing $u$ to the left side and constant terms to the right side. Subtract $8u$ from both sides of the equation.
$5u + 15 - 8u = 8u + 24 - 8u$

STEP 5

Simplify both sides of the equation by combining like terms.
$-3u + 15 = 24$

STEP 6

Next, we want to isolate $u$ completely. Subtract 15 from both sides of the equation to move the constant term to the right side.
$-3u + 15 - 15 = 24 - 15$

STEP 7

Simplify both sides of the equation.
$-3u = 9$

STEP 8

To solve for $u$ , divide both sides of the equation by $-3$ .
$\frac{-3u}{-3} = \frac{9}{-3}$

STEP 9

Simplify both sides of the equation to find the value of $u$ .
$u = -3$
The solution to the equation $5(u+3)=8u+24$ is $u = -3$ .

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