Question

How many solutions can be found for the linear equation?
4(x+5)-5 = 8x+18/2

A. no solutions

B. one solution

C. two solutions

D. infinitely many solutions

Answer 1

To find the number of solutions for the linear equation, we need to simplify the equation and see how many variable terms are left.

Starting with the given equation:
4(x + 5) - 5 = 8x + 18/2

First, distribute the 4 on the left side of the equation:
4x + 20 - 5 = 8x + 9

Combine like terms on the left side:
4x + 15 = 8x + 9

Next, subtract 4x from both sides to isolate the variable terms:
15 = 4x + 9 - 8x

Combine like terms on the right side:
15 = -4x + 9

Then, subtract 9 from both sides:
15 - 9 = -4x + 9 - 9

Simplify:
6 = -4x

Finally, divide both sides by -4 to solve for x:
6/-4 = -4x/-4

Simplify:
-3/2 = x

Therefore, there is only one solution for the linear equation.

The correct answer is B. one solution.