An equation is shown below:
4(2x - 5) = 4
Part A: How many solutions does this equation have? (4 points)
Part B: What are the solutions to this equation? Show your work. (6 points)
4(2x - 5) = 4
8x - 20 = 4
8x = 24
x = 3
To determine the number of solutions for the equation 4(2x - 5) = 4, we first want to simplify the equation. Here's how you can do that:
Part A:
Step 1: Distribute the 4 on the left side of the equation to eliminate the parentheses:
4 * 2x - 4 * 5 = 4
8x - 20 = 4
Step 2: Move the constant term (-20) to the other side of the equation by adding 20 to both sides:
8x - 20 + 20 = 4 + 20
8x = 24
Step 3: Divide both sides of the equation by the coefficient of x (8):
8x/8 = 24/8
x = 3
Since we ended up with a single solution for x, the equation 4(2x - 5) = 4 has only one solution.
Part B:
To find the solution to the equation 4(2x - 5) = 4, we follow the steps we used in Part A and solve for x:
Step 1: Distribute the 4 on the left side of the equation to eliminate the parentheses:
4 * 2x - 4 * 5 = 4
8x - 20 = 4
Step 2: Move the constant term (-20) to the other side of the equation by adding 20 to both sides:
8x - 20 + 20 = 4 + 20
8x = 24
Step 3: Divide both sides of the equation by the coefficient of x (8):
8x/8 = 24/8
x = 3
Therefore, the solution to the equation 4(2x - 5) = 4 is x = 3.
Part A: To determine the number of solutions the equation has, we need to solve it first.
Part B: Let's solve the equation step by step:
Step 1: Distribute the 4 on the left side of the equation:
8x - 20 = 4
Step 2: Move the constant term to the right side of the equation by adding 20 to both sides:
8x = 4 + 20
8x = 24
Step 3: Divide both sides of the equation by 8 to isolate the variable x:
x = 24/8
x = 3
So the equation has one solution, which is x = 3.