Question

An equation is shown below: 5(2x − 3) = 15 Part A: How many solutions does this equation have? Part B: What are the solutions to this equation? Show your work.

Answer 1

Part A: This equation has only one solution.

Part B: The solution to the equation is x = 3.

Explanation:

To solve the equation 5(2x - 3) = 15, we can follow these steps:

Part A: Determining the number of solutions

Since this is a linear equation with one variable, it can have either one solution, infinitely many solutions, or no solution.

Part B: Solving the equation

Let's solve the equation step by step:

Distribute the 5 on the left side of the equation:

5 * 2x - 5 * 3 = 15

10x - 15 = 15

Add 15 to both sides of the equation to isolate the variable term:

10x - 15 + 15 = 15 + 15

10x = 30

Divide both sides of the equation by 10 to solve for x:

(10x) / 10 = 30 / 10

x = 3

Therefore, the solution to the equation 5(2x - 3) = 15 is x = 3.

To summarize:

Part A: This equation has only one solution.

Part B: The solution to the equation is x = 3.

Answer 2

It has one solution

Explanation:

5(2x-3)=15

10x-15=15

10x=15+15

10x=30

divide both sides by 10

10x/10=30/10

x=3