Question

for each part below, solve the equation.
(a) solve for w.
$2(w + 1) + 4w = 3(2w - 1) + 8$
no solution
$w = \square$
all real numbers are solutions
(b) solve for x.
$3(x - 2) - 4x = 2(x - 9)$
no solution
$x = \square$
all real numbers are solutions

Explanation:

Step1: Expand both sides

Left: $2(w+1)+4w = 2w+2+4w = 6w+2$
Right: $3(2w-1)+8 = 6w-3+8 = 6w+5$

Step2: Simplify the equation

$6w+2 = 6w+5$
Subtract $6w$ from both sides: $2=5$

Step3: Analyze the result

$2=5$ is a false statement, so no solution exists for (a).

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Step1: Expand both sides

Left: $3(x-2)-4x = 3x-6-4x = -x-6$
Right: $2(x-9) = 2x-18$

Step2: Isolate the variable $x$

$-x-6 = 2x-18$
Add $x$ to both sides: $-6 = 3x-18$
Add 18 to both sides: $12 = 3x$

Step3: Solve for $x$

$x = \frac{12}{3}=4$

Answer:

(a) No solution
(b) $x = 4$