Question

for each part below, solve the equation.
(a) solve for u.
8(u - 1) - 4 = 4(2u - 3)
no solution
u =
all real numbers are solutions
(b) solve for w.
-8(w + 1) = 2(1 - 4w) - 9
no solution
w =
all real numbers are solutions

Explanation:

Part (a)

Step1: Expand both sides

Expand the left side: \(8(u - 1)-4 = 8u-8 - 4=8u - 12\)
Expand the right side: \(4(2u - 3)=8u-12\)

Step2: Compare both sides

We have \(8u - 12=8u - 12\). Subtracting \(8u\) from both sides gives \(- 12=-12\), which is always true. So all real numbers are solutions.

Part (b)

Step1: Expand both sides

Expand the left side: \(-8(w + 1)=-8w-8\)
Expand the right side: \(2(1 - 4w)-9=2 - 8w-9=-8w - 7\)

Step2: Solve for \(w\)

Set the expanded forms equal: \(-8w-8=-8w - 7\). Add \(8w\) to both sides: \(-8=-7\), which is false. Thus, there is no solution.

Answer:

All real numbers are solutions