Question

for each part below, solve the equation. (a) solve for v. 5(v + 1) - v = 4(v - 1) + 9 no solution v = all real numbers are solutions (b) solve for u. 2(u + 1) + 7 = 3(u - 2) + 2u no solution u = all real numbers are solutions

Explanation:

Part (a)

Step1: Expand both sides

$5v + 5 - v = 4v - 4 + 9$

Step2: Simplify each side

$4v + 5 = 4v + 5$

Step3: Isolate variable terms

Subtract $4v$ from both sides: $5 = 5$

Part (b)

Step1: Expand both sides

$2u + 2 + 7 = 3u - 6 + 2u$

Step2: Simplify each side

$2u + 9 = 5u - 6$

Step3: Move u terms to one side

Subtract $2u$ from both sides: $9 = 3u - 6$

Step4: Isolate constant terms

Add 6 to both sides: $15 = 3u$

Step5: Solve for u

Divide by 3: $u = \frac{15}{3} = 5$

Answer:

(a) All real numbers are solutions
(b) $u = 5$