Question

solve each equation. check your solution.

1. 9g - 14 = 2g
2. -6f + 13 = 2f - 11
3. 2.5h - 15 = 4h
4. 2z - 31 = -9z + 24
5. will averages 18 points a game and is the all - time scoring leader on his team with 483 points. tom averages 21 points a game and is currently second on the all - time scorers list with 462 points. if both players continue to play at the same rate, how many more games will it take until tom and will have scored the same number of total points?
6. eighteen less than three times a number is twice the number. define a variable, write an equation, and solve to find the number.

reason abstractly write an equation to find the value of x so that each pair of polygons has the same perimeter. then solve.
20.
21.

Explanation:

Step1: Solve equation 14 ($9g - 14=2g$)

Subtract $9g$ from both sides.
$9g - 14-9g=2g - 9g$
$-14=-7g$
Divide both sides by $- 7$.
$\frac{-14}{-7}=\frac{-7g}{-7}$
$g = 2$

Step2: Solve equation 15 ($-6f + 13=2f-11$)

Add $6f$ to both sides.
$-6f + 13+6f=2f-11 + 6f$
$13=8f-11$
Add 11 to both sides.
$13 + 11=8f-11 + 11$
$24=8f$
Divide both sides by 8.
$\frac{24}{8}=\frac{8f}{8}$
$f = 3$

Step3: Solve equation 16 ($2.5h-15 = 4h$)

Subtract $2.5h$ from both sides.
$2.5h-15-2.5h=4h-2.5h$
$-15 = 1.5h$
Divide both sides by 1.5.
$\frac{-15}{1.5}=\frac{1.5h}{1.5}$
$h=-10$

Step4: Solve equation 17 ($2z-31=-9z + 24$)

Add $9z$ to both sides.
$2z-31 + 9z=-9z + 24+9z$
$11z-31=24$
Add 31 to both sides.
$11z-31 + 31=24+31$
$11z=55$
Divide both sides by 11.
$\frac{11z}{11}=\frac{55}{11}$
$z = 5$

Step5: Solve problem 18

Let $x$ be the number of games played.
Will's total - points after $x$ games is $483+18x$.
Tom's total - points after $x$ games is $462 + 21x$.
Set them equal: $483+18x=462 + 21x$
Subtract $18x$ from both sides.
$483+18x-18x=462 + 21x-18x$
$483=462 + 3x$
Subtract 462 from both sides.
$483-462=462 + 3x-462$
$21=3x$
Divide both sides by 3.
$\frac{21}{3}=\frac{3x}{3}$
$x = 7$

Step6: Solve problem 19

Let the number be $n$.
The equation is $3n-18 = 2n$.
Subtract $2n$ from both sides.
$3n-18-2n=2n-2n$
$n-18=0$
Add 18 to both sides.
$n-18 + 18=0 + 18$
$n = 18$

Step7: Solve problem 20

Perimeter of the triangle: $(x + 4)+(x + 2)+(x + 5)=3x+11$
Perimeter of the rectangle: $2((x + 3)+(x + 1))=2(2x + 4)=4x+8$
Set them equal: $3x+11=4x + 8$
Subtract $3x$ from both sides.
$3x+11-3x=4x + 8-3x$
$11=x + 8$
Subtract 8 from both sides.
$11-8=x + 8-8$
$x = 3$

Step8: Solve problem 21

Perimeter of the pentagon: $5\times12x=60x$
Perimeter of the triangle: $(x + 7)+(x + 10)+(6x + 9)=8x+26$
Set them equal: $60x=8x+26$
Subtract $8x$ from both sides.
$60x-8x=8x+26-8x$
$52x=26$
Divide both sides by 52.
$\frac{52x}{52}=\frac{26}{52}$
$x=\frac{1}{2}$

Answer:

1. $g = 2$
2. $f = 3$
3. $h=-10$
4. $z = 5$
5. 7 games
6. $n = 18$
7. $x = 3$
8. $x=\frac{1}{2}$