Algebra 1 - 2.1-2.3 Review

One-Step Equations

100

Solve for b:

-7 = b - 3

b = -4

WORK
-7 = b - 3
-7 +3 = b - 3 +3
-4 = b

200

Solve for x:

x/3 = 2

x = 6

WORK
x/3 = 2
x/3 *3 = 2 *3
x = 6

300

Solve for x:

5x = 20

(When you see it written 5x that means the same thing as 5*x)

x = 4

WORK
5x = 20
5x/5 = 20/5
x = 4

400

Solve for m:

(4/5)*m = 28

m = 35

WORK
(4/5)*m = 28
(5/4)*(4/5)*m = 28*(5/4)
m = 35

500

Solve for p:

-2.54 = p + 7.17

p = -9.71

WORK
-2.54 = p + 7.17
-2.54- 7.17 = p + 7.17- 7.17
p = -9.71

Two-Step Equations

100

Solve for x:

2x + 3 = 15

(When you see it written 2x that means the same thing as 2*x)

x = 6

WORK
2x + 3 = 15
2x + 3 - 3 = 15 - 3
2x = 12
(2x)/2 = 12/2
x = 6

200

Solve for a:

(1/2)a + 5 = 18

a = 26

WORK
(1/2)a + 5 = 18
(1/2)a + 5 - 5 = 18 - 5
(1/2)a = 13
2*(1/2)a = 13*2
a = 26

300

Solve for t:

t - a = 3

t = 3 + a

400

Solve for x:

(x – 7)/3 = -12

x = -29

WORK
(x – 7)/3 = -12
3*((x – 7)/3)= -12*3
x – 7 = -36
x – 7 + 7= -36 + 7
x = -29

500

Solve for x:

9 = ax + 3

x = 6/a

Multi-Step Equations

100

Solve for m:

5 = 5m - 23 + 2m

m =4

WORK
5 = 5m - 23 + 2m
5 = 5m + 2m - 23
5 = 7m - 23
5 + 23 = 7m - 23 + 23
28 = 7m
28/7 = 7m/7
4 = m

200

Solve for x:

(x + 4) + 2x = 67

x = 21

WORK
(x + 4) + 2x = 67
x + 2x + 4 = 67 [addition is commutative]
3x + 4 = 67
3x + 4 - 4= 67 - 4
3x = 63
3x/3 = 63/3
x = 21

300

Solve for x:

-8(2x - 1) = 36

x = -7/4

WORK
-8(2x - 1) = 36
-16x + 8 = 36 [Distributive Property]
-16x + 8 - 8 = 36 - 8
-16x = 28
-16x/(-16) = 28/(-16)
x = -7/4

400

Solve for x:

3.5 - 0.02x = 1.24

x = 113

WORK
3.5 - 0.02x = 1.24
100*(3.5 - 0.02x) = 1.24*100
350 - 2x = 124 [Distributive Property]
350 - 350 - 2x = 124 - 350
-2x/(-2) = -226/(-2)
x = 113

500

Solve for x:

(3/4)x -2 = 10

x = 16

WORK

(3/4)x = 12

3x/4  = 12

3x = 36

x=12

Translating

100

Translate the equation x+7=15 into a sentence.

A number (x) increased by 7 is 15.

200

Translate the sentence “Five times a number is 35” into an equation.

5x=35

300

Translate the equation 3(x−4)=18 into a sentence.

Three times the difference of a number (x) and 4 is 18.

400

Translate the sentence “Seven less than twice a number is equal to 13” into an equation.

2x−7=13 

500

Translate the equation 4(x+3)=2x+9 into a sentence.

Four times the sum of a number (x) and 3 is equal to twice the number (x) increased by 9.

Word Problems

100

Solve:

Five friends equally split a restaurant bill that comes to $32.50. How much does each friend pay?

Each friend pays $6.50.

WORK

5x = 32.50

5x/5 = 32.50/5

x = 6.5 ~~~> $6.50

200

Solve:

You work for 4 hours on Saturday and 8 hours on Sunday. You receive a $50 bonus. You earn $164.00 total. How much did you earn per hour?

You earned $9.50 per hour.

WORK

4x + 8x + 50 = 164

12x + 50 = 164

12x + 50 - 50 = 164 - 50

12x = 114

12x/12 = 114/12

x = 9.5 ~~~> $9.50

300

Solve:

Sarah has 7 fewer than twice as many stickers as Jake. Sarah has 25 stickers. How many stickers does Jake have?

16 stickers

400

Solve

A rectangle has a perimeter of 54 cm. Its length is 3 cm more than its width. What are the dimensions of the rectangle?

Width = 12 cm, Length = 15 cm

500

Solve

A school club is selling T-shirts for $18 each. The club already has $75 in its account and wants to raise at least $300 total. What is the minimum number of T-shirts they need to sell?

13 T-shirts