Question

for each part below, solve the equation. (a) solve for y. 6(y + 1)-9 = 4(y - 1)+2y no solution y = all real numbers are solutions (b) solve for v. -4(v + 4)=3(v + 4)+7 no solution v = all real numbers are solutions

Explanation:

Step1: Expand both sides of (a)

Expand $6(y + 1)-9$ to $6y+6 - 9=6y - 3$, and expand $4(y - 1)+2y$ to $4y-4 + 2y=6y-4$.

Step2: Analyze the equation

The equation $6y - 3=6y-4$ simplifies to $-3=-4$ after subtracting $6y$ from both sides. This is a false statement, so there is no solution for (a).

Step3: Expand both sides of (b)

Expand $-4(v + 4)$ to $-4v-16$, and expand $3(v + 4)+7$ to $3v+12 + 7=3v+19$.

Step4: Solve for v

The equation $-4v-16=3v+19$ can be solved by adding $4v$ to both sides: $-16 = 7v+19$. Then subtract 19 from both sides: $-16-19=7v$, so $-35 = 7v$. Divide both sides by 7, we get $v=-5$.

Answer:

(a) No solution
(b) $v = - 5$