Question

for each part below, solve the equation.
(a) solve for u.
5(2 - u) - u = 2(u + 1)
no solution
u =
all real numbers are solutions
(b) solve for y.
4(y - 3) - 6y = -2(y + 6)
no solution
y =
all real numbers are solutions

Explanation:

Part (a)

Step1: Expand both sides

Expand \(5(2 - u)-u\) and \(2(u + 1)\).
Left side: \(5\times2-5u - u=10 - 6u\).
Right side: \(2u+2\).
Equation becomes \(10 - 6u=2u + 2\).

Step2: Isolate \(u\) terms

Add \(6u\) to both sides: \(10=8u + 2\).
Subtract 2: \(8 = 8u\).

Step3: Solve for \(u\)

Divide by 8: \(u = 1\).

Step1: Expand both sides

Expand \(4(y - 3)-6y\) and \(-2(y + 6)\).
Left side: \(4y-12-6y=-2y - 12\).
Right side: \(-2y-12\).

Step2: Analyze the equation

We get \(-2y - 12=-2y - 12\).
Subtract \(-2y - 12\) from both sides: \(0 = 0\), which is always true.

Answer:

\(u = 1\)

Part (b)