Question

for each part below, solve the equation.
(a) solve for w.
3(w - 2) + 5 = 2(3w - 5)
no solution
w =
all real numbers are solutions
(b) solve for u.

Explanation:

Part (a)

Step1: Expand both sides

Expand the left side: \(3(w - 2)+5 = 3w-6 + 5=3w - 1\)
Expand the right side: \(2(3w - 5)=6w-10\)
So the equation becomes \(3w - 1=6w - 10\)

Step2: Move terms with \(w\) to one side

Subtract \(3w\) from both sides: \(3w - 1-3w=6w - 10-3w\)
Simplify: \(-1 = 3w-10\)

Step3: Solve for \(w\)

Add 10 to both sides: \(-1 + 10=3w-10 + 10\)
Simplify: \(9 = 3w\)
Divide both sides by 3: \(w=\frac{9}{3}=3\)

Answer:

\(w = 3\)