7. 3(5y + 1) = 18y\n8. 4 - 3x = 8 - 4x\n9. 8(2w - 2) = 7(3w + 2)\n10. 3(5x + 2) = 2(3x - 6)\n11. 6(m - 1) =…

Explanation:

Step1: Solve equation 7. Expand left - hand side

$3(5y + 1)=15y + 3$, so the equation becomes $15y+3 = 18y$.

Step2: Isolate the variable terms

Subtract $15y$ from both sides: $15y+3-15y=18y - 15y$, which simplifies to $3 = 3y$.

Step3: Solve for $y$

Divide both sides by 3: $\frac{3}{3}=\frac{3y}{3}$, so $y = 1$.

Step4: Solve equation 8. Isolate the variable terms

Add $4x$ to both sides: $4-3x + 4x=8-4x+4x$, which gives $4 + x=8$.

Step5: Solve for $x$

Subtract 4 from both sides: $4 + x-4=8 - 4$, so $x = 4$.

Step6: Solve equation 9. Expand both sides

$8(2w - 2)=16w-16$ and $7(3w + 2)=21w + 14$. The equation is $16w-16=21w + 14$.

Step7: Isolate the variable terms

Subtract $16w$ from both sides: $16w-16-16w=21w + 14-16w$, getting $-16 = 5w+14$.

Step8: Further isolate the variable

Subtract 14 from both sides: $-16-14=5w+14 - 14$, so $-30 = 5w$.

Step9: Solve for $w$

Divide both sides by 5: $\frac{-30}{5}=\frac{5w}{5}$, so $w=-6$.

Step10: Solve equation 10. Expand both sides

$3(5x + 2)=15x+6$ and $2(3x - 6)=6x-12$. The equation is $15x + 6=6x-12$.

Step11: Isolate the variable terms

Subtract $6x$ from both sides: $15x + 6-6x=6x-12-6x$, getting $9x+6=-12$.

Step12: Further isolate the variable

Subtract 6 from both sides: $9x+6-6=-12 - 6$, so $9x=-18$.

Step13: Solve for $x$

Divide both sides by 9: $\frac{9x}{9}=\frac{-18}{9}$, so $x=-2$.

Step14: Solve equation 11. Expand both sides

$6(m - 1)=6m-6$ and $3(3m + 5)=9m + 15$. The equation is $6m-6=9m + 15$.

Step15: Isolate the variable terms

Subtract $6m$ from both sides: $6m-6-6m=9m + 15-6m$, getting $-6 = 3m+15$.

Step16: Further isolate the variable

Subtract 15 from both sides: $-6-15=3m+15 - 15$, so $-21 = 3m$.

Step17: Solve for $m$

Divide both sides by 3: $\frac{-21}{3}=\frac{3m}{3}$, so $m=-7$.

Step18: Solve equation 12. Expand both sides

$7(p + 3)+9=7p+21 + 9=7p+30$ and $5(p - 2)-3p=5p-10-3p=2p-10$. The equation is $7p+30=2p-10$.

Step19: Isolate the variable terms

Subtract $2p$ from both sides: $7p+30-2p=2p-10-2p$, getting $5p+30=-10$.

Step20: Further isolate the variable

Subtract 30 from both sides: $5p+30-30=-10 - 30$, so $5p=-40$.

Step21: Solve for $p$

Divide both sides by 5: $\frac{5p}{5}=\frac{-40}{5}$, so $p=-8$.

Answer:

$y = 1$, $x = 4$, $w=-6$, $x=-2$, $m=-7$, $p=-8$