Question

An equation is shown below:

5x + 3(x - 5) = 6x + 2x - 15

Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)

Part B: Name one property you used to solve this equation. (4 points)

Answer 1

5x + 3(x - 5) = 6x + 2x - 15

5x + 3x - 15 = 8x - 15

8x - 8x = -15 + 15

0 = 0

Since, both sides are equal, this equation is true for all x.

Part B:

One property used is distributive property. 

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

Answer 2

The equation has no solutions. The property used to solve the equation is the additive property of variables.

Solving one-variable equations

The solution of the equation is as follows;

• 5x + 3(x - 5) = 6x + 2x - 15

• 8x -15 = 8x -15.

From the equation above, it follows that;

Since, the right hand side and left hand side of the equation are equal, the equation has no solution.

Read more on one-variable equations;

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