Unit 2 Review (6th grade)

Simplify Equations

100

7x² + 4x² - 5x²

11x² + -5x²

6x²

200

-8a³ + 6a³ - 9a³

-17a³ + 6a³

-11a³

300

4(3r²t)

12r²t

400

5(k+2)

5k + 10

500

-2(3b+4)

-6b+-8

Solve and check

100

x+11=24

x+11=24
-11 from each side
x=13

Check:
x+11=24
13+11=24
24=24

200

y-18=-7

y-18=-7
add 18 to each side
y=11

Check:
y-18=-7
11+-18=-7
-7=-7

300

8a=-64

8a=-64
divide by 8 on each side
a=-8

Check:
8a=-64
8(-8)=-64

-64=-64

400

3(2y-4) + 12

6y-12 + 12
6y

500

-4 + 6(4x+1) - 4x

-4 + 24x + 6 - 4x
Combine like terms
20x +-4 + 6
20x + 2

Two-sided Equations

100

9x+3=48

9x+3=48
subtract 3 from each side
9x=45
divide each side by 9
x=5

200

2+3y=-13

2+3y=-13
subtract 2 from each side
3y=-15
divide by 3 on each side
y=-5

300

-2 + 11a = 20

-2 + 11a = 20
add 2 to each side
11a=22
divide by 11 on each side
a=2

400

18 -4p = -2

18 -4p = -2
subtract 18 from each side
-4p = -20
divide b -4 on each side
p=5

500

-2p + 5p = 3 - 21

-2p + 5p = 3 - 21
combine like terms
3p=-18
divide by 3 on each side
p=-6

Word Problems

100

A trail walker descends 80 meters, then climbs y meters to reach 40 meters below the starting point.

Write and solve the equation.

-80 + y = 40
add 80 to each side
y=120 meters

200

A diver is at -90 meters.  He rises x meters to reach -40 meters.

Write and solve the equation.

-90 + x = -40
add 90 to each side
x=50 meters

300

Syracuse's winter temperature was -18 degrees Fahrenheit. It rose t degrees to reach 3 degrees Fahrenheit.

-18 + t = 3
add 18 to each side
t= 21 degrees Fahrenheit

400

A scuba diver is at -30 meters. After diving d meters further, the depth is -50 meters.

Write an equation and solve.

-30 + d = -50
add 30 to each side
d=-20 meters

500

Every Wednesday is "treat day" at the office. Roger brings the treats and buys two treat items for each employee plus 4 extras.  If he brings 34 donuts, how many employees are there?

34=2n+4
subtract 4 from each side
30=2n
divide by 2 on each side
15=n

There are 15 employees

Distributive Property

100

6(x+3) - 2(2+5)

6(x+3) - 2(2+5)
6x + 18 -4 + -10
6x + 14 + -10
6x + 4

200

-3(a-1)+7(a+4)

-3(a-1)+7(a+4)
-3a + 3 +7a + 28
4a + 31

300

8(m+3)-5(m-2)

8(m+3)-5(m-2)
8m + 24 -5m + 10
3m + 34

400

3(2n-1) = 3(n+3)

3(2n-1) = 3(n+3)
6n-3=3n+9
add 3 to each side
6n=3n+12
subtract 3n from each side
3n=12
n=4

500

6 + 10d - 19 = 2(3d+4) - 1

6 + 10d - 19 = 2(3d+4) - 1
-13 + 10d = 6d+8 - 1
-13 + 10d = 6d + 7
-20 + 10d = 6d
-20 = -4d
5=d