Question

An equation is shown below:5(2x − 3) = 5Part A: How many solutions does this equation have? (4 points)Part B: What are the solutions to this equation? Show your work.

Answer 1

Part A

The given equation is

`5(2x\text{ -3\rparen=5}`

as there is only one variable, the equation either has 1 solution or no solution. However, note that on the left we have a polynomial of degree 1 (a line), whenever we make it equal to a constant, we always have a solution. So in this case the solution is 1.

Part B

Now, to solve this equation first we divide both sides by 5. So we get

`2x\text{ -3=1}`

Then, we add 3 on both sides to get

`2x=1+3=4`

Finally we divide both sides by 2 to get

`x=(4)/(2)=2`

so the unique solution of the equation is x=2