Question

1. use the distributive property to solve the equation 28 - (3x + 4) = 2(x + 6) + x.

28 - x - = 2x + + x
24 - x = x +
24 - x =
x =
x =

1. use the distributive property to solve the equation 3(x - 6) + 6 = 5x - 6.

x - + 6 = 5x -
x - = 5x -
x - =
x =
x =

1. what is the solution to -2.5(4x - 4) = -6?

12 what is the solution to the equation 3(x + 2) = 2(x + 5)?

1. solve the equation $\frac{1}{6}(x - 5)=\frac{1}{2}(x + 6)$.
2. solve the equation 0.6(x + 2) = 0.55(2x + 3).

3 - 5 solve multistep equations

Explanation:

Step1: Apply distributive property on equation 9

$28-(3x + 4)=28-3x - 4=24-3x$ and $2(x + 6)+x=2x+12 + x=3x + 12$. So the equation becomes $24-3x=3x + 12$.

Step2: Move like - terms to one side

Add $3x$ to both sides: $24=3x+12 + 3x$, which simplifies to $24=6x + 12$.

Step3: Isolate the term with $x$

Subtract 12 from both sides: $24-12=6x$, so $12 = 6x$.

Step4: Solve for $x$

Divide both sides by 6: $x=\frac{12}{6}=2$.

Step5: Apply distributive property on equation 10

$3(x - 6)+6=3x-18 + 6=3x-12$ and the right - hand side is $5x-6$. So the equation is $3x-12=5x-6$.

Step6: Move like - terms to one side

Subtract $3x$ from both sides: $-12=5x-6-3x$, which simplifies to $-12=2x-6$.

Step7: Isolate the term with $x$

Add 6 to both sides: $-12 + 6=2x$, so $-6=2x$.

Step8: Solve for $x$

Divide both sides by 2: $x=\frac{-6}{2}=-3$.

Step9: Solve equation 11

First, apply the distributive property: $-2.5(4x - 4)=-10x+10$. The equation becomes $-10x + 10=-6$.

Step10: Isolate the term with $x$

Subtract 10 from both sides: $-10x=-6 - 10=-16$.

Step11: Solve for $x$

Divide both sides by $-10$: $x=\frac{-16}{-10}=\frac{8}{5}=1.6$.

Step12: Solve equation 12

Apply the distributive property: $3(x + 2)=3x+6$ and $2(x + 5)=2x + 10$. The equation is $3x+6=2x + 10$.

Step13: Move like - terms to one side

Subtract $2x$ from both sides: $3x-2x+6=10$, so $x+6=10$.

Step14: Solve for $x$

Subtract 6 from both sides: $x=10 - 6 = 4$.

Step15: Solve equation 13

Multiply both sides of $\frac{1}{6}(x - 5)=\frac{1}{2}(x + 6)$ by 6 to get $x-5 = 3(x + 6)$.

Step16: Apply distributive property

$x-5=3x+18$.

Step17: Move like - terms to one side

Subtract $x$ from both sides: $-5=3x+18-x$, which simplifies to $-5=2x+18$.

Step18: Isolate the term with $x$

Subtract 18 from both sides: $-5-18=2x$, so $-23=2x$.

Step19: Solve for $x$

Divide both sides by 2: $x=-\frac{23}{2}=-11.5$.

Step20: Solve equation 14

Apply the distributive property: $0.6(x + 2)=0.6x+1.2$ and $0.55(2x + 3)=1.1x+1.65$. The equation is $0.6x+1.2=1.1x+1.65$.

Step21: Move like - terms to one side

Subtract $0.6x$ from both sides: $1.2=1.1x+1.65-0.6x$, which simplifies to $1.2=0.5x+1.65$.

Step22: Isolate the term with $x$

Subtract 1.65 from both sides: $1.2-1.65=0.5x$, so $-0.45=0.5x$.

Step23: Solve for $x$

Divide both sides by 0.5: $x=\frac{-0.45}{0.5}=-0.9$.

Answer:

Equation 9: $x = 2$
Equation 10: $x=-3$
Equation 11: $x = 1.6$
Equation 12: $x = 4$
Equation 13: $x=-11.5$
Equation 14: $x=-0.9$