Question

Consider the following linear equation:
1/8(z+3)=4/5(z+1/8)
Solve the above linear equation. Simplify your answer.

Answer 1

I've gotcha! ..just let me type it all out.

Answer 2

if you want to get rid of the fractions, you can multiply the equation by 40

-> 5(z+3) = 32(z+ 1/8)

Answer 3

Okay, I hope you can read this:

First, simplify the equations:
\[1/8(z) + 3/8 = 4/5(z) + 4/40\]

Next, collect like-terms (z's) on one side of the equation:
\[1/8(z) - 4/5(z) = 4/40 - 3/8\]

Multiply through to get a common denominator (of 40):
\[5/40(z) - 32/40(z) = 4/40 - 15/40\]

Simplify each side by subtracting the like terms on each side:
\[-27/40z = -11/40\]

Divide the -27/40 into -11/40, or multiply by the reciprocal:
\[z = (-11/40) * (40/-27)\]

..and there you have it.
z = -11/-27
or just 11/27.