Question

name
lesson 3 homework practice
solve equations with variables on each side
solve each equation. check your solution.

1. 9m + 14 = 2m
2. 13x = 32 + 5x
3. 8d - 25 = 3d
4. t - 27 = 4t
5. 7p - 5 = 6p + 8
6. 11z - 5 = 9z + 7
7. 12 - 5h = h + 6
8. 4 - 7f = f - 12
9. -6y + 17 = 3y - 10
10. 3x - 32 = -7x + 28
11. 3.2a - 16 = 4a
12. 16.8 - v = 6v

define a variable, write an equation, and solve to determine each number.

1. fourteen less than five times a number is three times the number.
2. twelve more than seven times a number equals the number less six.

write an equation to determine the value of x so that each pair of polygons has the same perimeter.
15.
16.

Explanation:

Step1: Solve equation 1 ($9m + 14=2m$)

Subtract $2m$ from both sides and subtract 14 from both sides.
$9m-2m=- 14$
$7m=-14$
Then divide both sides by 7: $m = - 2$

Step2: Solve equation 2 ($13x=32 + 5x$)

Subtract $5x$ from both sides: $13x-5x=32$
$8x=32$
Divide both sides by 8: $x = 4$

Step3: Solve equation 3 ($8d-25 = 3d$)

Subtract $3d$ from both sides: $8d-3d=25$
$5d=25$
Divide both sides by 5: $d = 5$

Step4: Solve equation 5 ($7p-5=6p + 8$)

Subtract $6p$ from both sides and add 5 to both sides: $7p-6p=8 + 5$
$p=13$

Step5: Solve equation 7 ($12-5h=h + 6$)

Add $5h$ to both sides and subtract 6 from both sides: $12-6=h + 5h$
$6=6h$
Divide both sides by 6: $h = 1$

Step6: Solve equation 8 ($4-7f=f-12$)

Add $7f$ to both sides and add 12 to both sides: $4 + 12=f+7f$
$16=8f$
Divide both sides by 8: $f = 2$

Step7: Solve equation 9 ($-6y + 17=3y-10$)

Add $6y$ to both sides and add 10 to both sides: $17 + 10=3y+6y$
$27=9y$
Divide both sides by 9: $y = 3$

Step8: Solve equation 10 ($3x-32=-7x + 28$)

Add $7x$ to both sides and add 32 to both sides: $3x+7x=28 + 32$
$10x=60$
Divide both sides by 10: $x = 6$

Step9: Solve equation 11 ($3.2a-16=4a$)

Subtract $3.2a$ from both sides: $-16=4a-3.2a$
$-16 = 0.8a$
Divide both sides by $0.8$: $a=-20$

Step10: Solve equation 12 ($16.8-v=6v$)

Add $v$ to both sides: $16.8=6v + v$
$16.8=7v$
Divide both sides by 7: $v = 2.4$

Step11: Solve equation 13 ("Fourteen less than five times a number is three times the number")

Let the number be $x$. The equation is $5x-14 = 3x$.
Subtract $3x$ from both sides and add 14 to both sides: $5x-3x=14$
$2x=14$
Divide both sides by 2: $x = 7$

Step12: Solve equation 14 ("Twelve more than seven times a number equals the number less six")

Let the number be $x$. The equation is $7x + 12=x-6$.
Subtract $x$ from both sides and subtract 12 from both sides: $7x-x=-6-12$
$6x=-18$
Divide both sides by 6: $x=-3$

Step13: Solve equation 15 (perimeter of triangle = perimeter of rectangle)

Perimeter of triangle: $(x + 6)+(x + 3)+(x + 9)=3x+18$
Perimeter of rectangle: $2(x + 4)+2(x + 1)=2x+8+2x + 2=4x + 10$
Set them equal: $3x+18=4x + 10$
Subtract $3x$ from both sides and subtract 10 from both sides: $18-10=4x-3x$
$x = 8$

Step14: Solve equation 16 (perimeter of hexagon = perimeter of triangle)

Perimeter of hexagon: $6\times5x=30x$
Perimeter of triangle: $(x + 14)+(8x)+(x + 14)=10x+28$
Set them equal: $30x=10x+28$
Subtract $10x$ from both sides: $30x-10x=28$
$20x=28$
Divide both sides by 20: $x = 1.4$

Answer:

$m=-2,x = 4,d = 5,p=13,h = 1,f = 2,y = 3,x = 6,a=-20,v = 2.4,x = 7,x=-3,x = 8,x = 1.4$