Question

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

Explanation:

Step1: Expand both sides of the equation in (a)

-2(w + 2)+7 = -2w-4 + 7=-2w + 3, and 3(w + 6)=3w+18. So the equation becomes -2w + 3=3w+18.

Step2: Move the terms with w to one - side

Add 2w to both sides: 3=3w + 2w+18, which simplifies to 3 = 5w+18.

Step3: Isolate the term with w

Subtract 18 from both sides: 3-18=5w, so - 15 = 5w.

Step4: Solve for w

Divide both sides by 5: w=-3.

Step5: Expand both sides of the equation in (b)

-2(x + 6)+6x=-2x-12 + 6x = 4x-12, and 4(x - 3)=4x-12.

Step6: Analyze the equation

The left - hand side 4x-12 is equal to the right - hand side 4x-12 for all real values of x. So all real numbers are solutions.

Answer:

(a) w = - 3
(b) All real numbers are solutions