Question

for each part below, solve the equation.
(a) solve for w.
$2(w + 1) + 7 = 3(w - 2) + 2w$
no solution
$w = \square$
all real numbers are solutions
(b) solve for x.
$-2(x + 6) + 6x = 4(x - 3)$
no solution
$x = \square$
all real numbers are solutions

Explanation:

Part (a)

Step1: Expand both sides

$2w + 2 + 7 = 3w - 6 + 2w$

Step2: Simplify both sides

$2w + 9 = 5w - 6$

Step3: Isolate w terms

$9 + 6 = 5w - 2w$

Step4: Solve for w

$15 = 3w \implies w = \frac{15}{3} = 5$

Part (b)

Step1: Expand both sides

$-2x - 12 + 6x = 4x - 12$

Step2: Simplify left side

$4x - 12 = 4x - 12$

Step3: Analyze equivalence

Subtract $4x - 12$ from both sides: $0 = 0$

Answer:

(a) $w = 5$
(b) All real numbers are solutions