Question

for each part below, solve the equation.
(a) solve for x.
-3(x + 5) + 5x = 2(x - 6)
no solution
x =
all real numbers are solutions
(b) solve for v.
3(v + 2) + 2v = 7(v - 1) + 9
no solution
v =
all real numbers are solutions

Explanation:

Part (a)

Step1: Expand both sides

Expand the left - hand side: \(-3(x + 5)+5x=-3x-15 + 5x=2x-15\)
Expand the right - hand side: \(2(x - 6)=2x-12\)
So the equation becomes \(2x-15 = 2x-12\)

Step2: Subtract \(2x\) from both sides

Subtract \(2x\) from both sides of the equation \(2x-15 = 2x-12\):
\(2x-2x-15=2x-2x - 12\)
Simplify to get \(-15=-12\), which is a false statement.

Step1: Expand both sides

Expand the left - hand side: \(3(v + 2)+2v=3v+6 + 2v=5v+6\)
Expand the right - hand side: \(7(v - 1)+9=7v-7 + 9=7v + 2\)
So the equation becomes \(5v+6=7v + 2\)

Step2: Move like terms together

Subtract \(5v\) from both sides: \(5v-5v + 6=7v-5v+2\), which gives \(6 = 2v+2\)
Subtract 2 from both sides: \(6 - 2=2v+2-2\), so \(4 = 2v\)

Step3: Solve for \(v\)

Divide both sides by 2: \(\frac{4}{2}=\frac{2v}{2}\), so \(v = 2\)

Answer:

No solution

Part (b)