Question

practice & problem solving
leveled practice in 8 and 9, solve each equation.

1. 6 - 4x = 6x - 8x + 2

6 - 4x =
6 =
=
= x

1. $\frac{5}{3}x+\frac{1}{3}x = 13\frac{1}{3}+\frac{8}{3}x$

x = 13\frac{1}{3}+\frac{8}{3}x
= \frac{8}{3}x - x
$-\frac{40}{3}=$ x
$cdot(-\frac{40}{3})=$ $cdot\frac{2}{3}x$
= x

1. two towns have accumulated different amounts of snow. in town 1, the snow depth is increasing by $3\frac{1}{2}$ inches every hour. in town 2, the snow depth is increasing by $2\frac{1}{4}$ inches every hour. in how many hours will the snowfalls of the towns be equal?
2. solve the equation 5.3g + 9 = 2.3g + 15.

a. find the value of g.
b. explain how you can check that the value you found for g is correct. if your check does not work, does that mean that your result is incorrect? explain.

1. solve the equation 6 - 6x = 5x - 9x - 2.
2. model with math the population of one town in florida is 43,425. about 125 people move out of the town each month. each month, 200 people on average move into town. a nearby town has a population of 45,000. it has no one moving in and an average of 150 people moving away every month. in about how many months will the population of the towns be equal? write an equation that represents this situation and solve.

Explanation:

8. Solve the equation $6 - 4x=6x - 8x + 2$

Step1: Combine like - terms on right side

Combine $6x$ and $-8x$ on the right - hand side of the equation. $6x-8x=-2x$, so the equation becomes $6 - 4x=-2x + 2$.

Step2: Add $4x$ to both sides

To get all the $x$ terms on one side, add $4x$ to both sides. $6-4x + 4x=-2x+4x + 2$, which simplifies to $6 = 2x+2$.

Step3: Subtract 2 from both sides

Subtract 2 from both sides to isolate the term with $x$. $6 - 2=2x+2 - 2$, resulting in $4 = 2x$.

Step4: Divide both sides by 2

Divide both sides by 2 to solve for $x$. $\frac{4}{2}=\frac{2x}{2}$, so $x = 2$.

Step1: Combine like - terms on left side

Combine $\frac{5}{3}x$ and $\frac{1}{3}x$ on the left - hand side. $\frac{5}{3}x+\frac{1}{3}x=\frac{5 + 1}{3}x=\frac{6}{3}x = 2x$. So the equation is $2x=\frac{40}{3}+\frac{8}{3}x$.

Step2: Subtract $\frac{8}{3}x$ from both sides

$2x-\frac{8}{3}x=\frac{40}{3}+\frac{8}{3}x-\frac{8}{3}x$. Convert $2x$ to $\frac{6}{3}x$, then $\frac{6}{3}x-\frac{8}{3}x=\frac{6 - 8}{3}x=-\frac{2}{3}x$. So $-\frac{2}{3}x=\frac{40}{3}$.

Step3: Multiply both sides by $-\frac{3}{2}$

$-\frac{3}{2}\times(-\frac{2}{3}x)=-\frac{3}{2}\times\frac{40}{3}$. On the left side, $-\frac{3}{2}\times(-\frac{2}{3}x)=x$, and on the right side, $-\frac{3}{2}\times\frac{40}{3}=-20$. So $x=-20$.

Step1: Set up the equation

$5 + 3.5t=6+2.25t$.

Step2: Subtract $2.25t$ from both sides

$5 + 3.5t-2.25t=6+2.25t-2.25t$, which simplifies to $5 + 1.25t=6$.

Step3: Subtract 5 from both sides

$5-5 + 1.25t=6 - 5$, resulting in $1.25t=1$.

Step4: Divide both sides by $1.25$

Since $1.25=\frac{5}{4}$, $t=\frac{1}{\frac{5}{4}}=\frac{4}{5}=0.8$ hours.

Answer:

$x = 2$

9. Solve the equation $\frac{5}{3}x+\frac{1}{3}x=13\frac{1}{3}+\frac{8}{3}x$

First, convert $13\frac{1}{3}$ to an improper fraction: $13\frac{1}{3}=\frac{40}{3}$.