Answered

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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.

Sagot :

Part A

The given equation is

[tex]5(2x\text{ -3\rparen=5}[/tex]

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

[tex]2x\text{ -3=1}[/tex]

Then, we add 3 on both sides to get

[tex]2x=1+3=4[/tex]

Finally we divide both sides by 2 to get

[tex]x=\frac{4}{2}=2[/tex]

so the unique solution of the equation is x=2

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