Kalyn was given the following equation.

8(1.75x−3)=0.5(10x+24)8(1.75x−3)=0.5(10x+24)

What is the solution to the equation?

A.44

B.33

C.−43−43

D.00

To solve the equation \( 8(1.75x - 3) = 0.5(10x + 24) \), let's follow these steps:

### Step 1: Expand both sides of the equation.
Expand the left side:
\[
8(1.75x - 3) = 8 \times 1.75x - 8 \times 3 = 14x - 24
\]
Expand the right side:
\[
0.5(10x + 24) = 0.5 \times 10x + 0.5 \times 24 = 5x + 12
\]
So the equation becomes:
\[
14x - 24 = 5x + 12
\]

### Step 2: Get all terms involving \(x\) on one side.
Subtract \(5x\) from both sides:
\[
14x - 5x - 24 = 12
\]
Simplify:
\[
9x - 24 = 12
\]

### Step 3: Solve for \(x\).
Add 24 to both sides:
\[
9x = 12 + 24
\]
\[
9x = 36
\]
Now, divide both sides by 9

Explore how to solve equations using the distributive property with a detailed step-by-step solution. This problem involves simplifying and balancing equations with variables. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Step 1: Expand both sides of the equation.

Step 2: Get all terms involving $x$ on one side.

Step 3: Solve for $x$ .

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