Question

for each part below, solve the equation.
(a) solve for w.
2(w - 3) - 5w = -3(w + 3)
no solution
w =
all real numbers are solutions
(b) solve for v.
-6(v + 1) = 2(1 - 3v) - 8
no solution
v =
all real numbers are solutions

Explanation:

Part (a)

Step1: Expand both sides

Expand the left - hand side: \(2(w - 3)-5w=2w-6 - 5w=-3w - 6\)
Expand the right - hand side: \(-3(w + 3)=-3w-9\)
So the equation becomes \(-3w-6=-3w - 9\)

Step2: Add \(3w\) to both sides

Add \(3w\) to both sides of the equation: \(-3w+3w - 6=-3w + 3w-9\)
Simplify to get \(-6=-9\)
Since \(-6
eq - 9\), this is a contradiction.

Step1: Expand both sides

Expand the left - hand side: \(-6(v + 1)=-6v-6\)
Expand the right - hand side: \(2(1 - 3v)-8=2-6v - 8=-6v-6\)
So the equation becomes \(-6v-6=-6v - 6\)

Step2: Add \(6v\) to both sides

Add \(6v\) to both sides of the equation: \(-6v+6v - 6=-6v + 6v-6\)
Simplify to get \(-6=-6\)
This is a true statement for all values of \(v\).

Answer:

No solution

Part (b)