Question

operations for solving equations with the variable on both sides - item 35074
solve each equation.
2a = -2 + 4(a + 3)
a =
-4b = -5(3 - b) + 6
b =

Explanation:

Step1: Expand the right - hand side of the first equation

Expand $4(a + 3)$ in $2a=-2 + 4(a + 3)$ using the distributive property $c(a + b)=ca+cb$. So $4(a + 3)=4a+12$, and the equation becomes $2a=-2 + 4a+12$.

Step2: Combine like terms on the right - hand side

Combine $-2$ and $12$ on the right - hand side. $2a=4a + 10$.

Step3: Move the variable terms to one side

Subtract $4a$ from both sides: $2a-4a=4a + 10-4a$. This gives $-2a=10$.

Step4: Solve for $a$

Divide both sides by $-2$: $a=\frac{10}{-2}=-5$.

Step5: Expand the right - hand side of the second equation

Expand $-5(3 - b)$ in $-4b=-5(3 - b)+6$ using the distributive property $c(a - b)=ca-cb$. So $-5(3 - b)=-15 + 5b$, and the equation becomes $-4b=-15 + 5b+6$.

Step6: Combine like terms on the right - hand side

Combine $-15$ and $6$ on the right - hand side. $-4b=5b-9$.

Step7: Move the variable terms to one side

Subtract $5b$ from both sides: $-4b-5b=5b-9-5b$. This gives $-9b=-9$.

Step8: Solve for $b$

Divide both sides by $-9$: $b=\frac{-9}{-9}=1$.

Answer:

$a=-5$
$b = 1$