Question

for each part below, solve the equation.
(a) solve for y.
3(y + 2) - y = 2(y - 1) + 5
no solution
y =
all real numbers are solutions
(b) solve for u.
-3(u + 1) + 7u = 4(u + 1) - 7
no solution
u =
all real numbers are solutions

Explanation:

Part (a)

Step1: Expand both sides

Left side: \(3(y + 2)-y=3y + 6 - y=2y+6\)
Right side: \(2(y - 1)+5=2y-2 + 5=2y + 3\)

Step2: Set equal and simplify

\(2y+6 = 2y+3\)
Subtract \(2y\) from both sides: \(6=3\), which is false.

Part (b)

Step1: Expand both sides

Left side: \(-3(u + 1)+7u=-3u-3 + 7u=4u-3\)
Right side: \(4(u + 1)-7=4u+4 - 7=4u-3\)

Step2: Compare sides

Left side \(4u - 3\) equals right side \(4u - 3\) for all \(u\).

Answer:

No solution