Question

How many solutions can be found for the linear equation?

4(x + 5) - 5 = 8x+18/2
A: no solution
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 both sides of the equation and then check if they are equal.

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

First, distribute the 4 on the left side:
4x + 20 - 5 = (8x + 18)/2

Combine like terms:
4x + 15 = (8x + 18)/2

Next, multiply every term by 2 to eliminate the fraction:
2(4x + 15) = 8x + 18

Distribute the 2 on the left side:
8x + 30 = 8x + 18

Subtract 8x from both sides to isolate the constants:
30 = 18

This equation is false, which means there are no solutions that will make both sides of the equation equal.

Therefore, the correct answer is A: no solution.