Question

for each part below, solve the equation.
(a) solve for x.
$4(x + 1) - x = 3(x - 1) + 3$
no solution
$x = \square$
all real numbers are solutions
(b) solve for w.
$4(w + 1) + w = 5(w - 1) + 9$
no solution
$w = \square$
all real numbers are solutions

Explanation:

Step1: Expand both sides

$4x + 4 - x = 3x - 3 + 3$

Step2: Simplify each side

$3x + 4 = 3x$

Step3: Isolate variable terms

$3x - 3x = -4$

Step4: Simplify to check consistency

$0 = -4$

(for part b):

Step1: Expand both sides

$4w + 4 + w = 5w - 5 + 9$

Step2: Simplify each side

$5w + 4 = 5w + 4$

Step3: Isolate variable terms

$5w - 5w = 4 - 4$

Step4: Simplify to check consistency

$0 = 0$

Answer:

(a) No solution
(b) All real numbers are solutions