Question

1. $z + 2z+3z = 36$ 8. $3w - 2w+w = 24$ 9. $0=a + 25+4a$ 10. $7(m - 1)=-63$ 11. $8(q + 7)=-72$ 12. $12(a + 7)=96$

Explanation:

Step1: Simplify the left - hand side of equation 7

Combine like terms: $z + 2z+3z=(1 + 2 + 3)z=6z$. So the equation becomes $6z = 36$.

Step2: Solve for $z$ in equation 7

Divide both sides by 6: $z=\frac{36}{6}=6$.

Step3: Simplify the left - hand side of equation 8

Combine like terms: $3w-2w + w=(3-2 + 1)w=2w$. So the equation becomes $2w = 24$.

Step4: Solve for $w$ in equation 8

Divide both sides by 2: $w=\frac{24}{2}=12$.

Step5: Combine like terms in equation 9

Combine like terms: $0=a + 25+4a$ gives $0=(1 + 4)a+25$, so $0 = 5a+25$.

Step6: Solve for $a$ in equation 9

Subtract 25 from both sides: $-25 = 5a$. Then divide both sides by 5: $a=\frac{-25}{5}=-5$.

Step7: Solve equation 10

First, distribute the 7: $7(m - 1)=7m-7$. So $7m-7=-63$.

Step8: Solve for $m$ in equation 10

Add 7 to both sides: $7m=-63 + 7=-56$. Then divide both sides by 7: $m=\frac{-56}{7}=-8$.

Step9: Solve equation 11

First, distribute the 8: $8(q + 7)=8q+56$. So $8q+56=-72$.

Step10: Solve for $q$ in equation 11

Subtract 56 from both sides: $8q=-72-56=-128$. Then divide both sides by 8: $q=\frac{-128}{8}=-16$.

Step11: Solve equation 12

First, distribute the 12: $12(a + 7)=12a+84$. So $12a+84 = 96$.

Step12: Solve for $a$ in equation 12

Subtract 84 from both sides: $12a=96 - 84 = 12$. Then divide both sides by 12: $a=\frac{12}{12}=1$.

Answer:

$z = 6$; $w = 12$; $a=-5$ (from equation 9); $m=-8$; $q=-16$; $a = 1$ (from equation 12)