Question

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

1. 6 - 4x = 6x - 8x + 2
2. $\frac{5}{3}x+\frac{1}{3}x = 13\frac{1}{3}+\frac{8}{3}x$
3. 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?
4. 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.

Step1: Combine like - terms on right side

$6-4x=6x - 8x+2$ simplifies to $6-4x=-2x + 2$.

Step2: Add $4x$ to both sides

$6-4x+4x=-2x + 2+4x$, which gives $6 = 2x+2$.

Step3: Subtract 2 from both sides

$6 - 2=2x+2 - 2$, so $4 = 2x$.

Step4: Divide both sides by 2

$\frac{4}{2}=\frac{2x}{2}$, and $x = 2$.

9.

Step1: Combine like - terms on left side

$\frac{5}{3}x+\frac{1}{3}x=\frac{5 + 1}{3}x=\frac{6}{3}x = 2x$. The equation becomes $2x=13\frac{1}{3}+\frac{8}{3}x$.

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

$2x-\frac{8}{3}x=13\frac{1}{3}+\frac{8}{3}x-\frac{8}{3}x$. Convert $2x$ to $\frac{6}{3}x$, then $\frac{6}{3}x-\frac{8}{3}x=-\frac{2}{3}x$. So $-\frac{2}{3}x = 13\frac{1}{3}=\frac{40}{3}$.

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

$x=\frac{40}{3}\times(-\frac{3}{2})=-20$.

10.

Step1: Set up equations

Let $h$ be the number of hours. In Town 1, the snow - depth equation is $y_1 = 5+3\frac{1}{2}h=5+\frac{7}{2}h$. In Town 2, the snow - depth equation is $y_2 = 6+2\frac{1}{4}h=6+\frac{9}{4}h$.

Step2: Set $y_1=y_2$

$5+\frac{7}{2}h=6+\frac{9}{4}h$.

Step3: Subtract $\frac{9}{4}h$ from both sides and subtract 5 from both sides

$\frac{7}{2}h-\frac{9}{4}h=6 - 5$. Convert $\frac{7}{2}h$ to $\frac{14}{4}h$, then $\frac{14}{4}h-\frac{9}{4}h = 1$, so $\frac{5}{4}h=1$.

Step4: Multiply both sides by $\frac{4}{5}$

$h = 4$.

11.

Answer:

$x = 2$