2026 Solving algebraic Equations

Solving One-Step Equations

Multiplying and Dividing Equations (word problems)

Solving Two-Step Equations

Adding and Subtracting Equations (word problems)

100

9 + n = 13

-9 = - 9

n = 4

100

m + 15 = 37

- 15 = -15

m = 37 - 15

m = 22

100

Nine-banded armadillos are always born in groups of 4. If there are 32 babies, what is the number of armadillos? Write an algebraic equation, and let m represent the number of mother armadillos.

4m = 32

/4 = /4

m = 32/4

m = 8 mothers

100

2x + 1 = 11

- 1 = -1

2x = 11 - 1

2x = 10

/2 = /2

x = 5

100

An emperor penguin is 45 inches tall. It is 24 inches taller than a rockhopper penguin. Write and solve an equation to find the height "h" (in inches) of a rockhopper penguin.

h + 24 = 45

- 24 = -24

h = 21 inches

200

m - 26 = 54

+26 = +26

m = 28

200

n - 42 = 18

+ 42 = + 42

n = 18 + 42

n = 60

200

The Empire State Building is 381 m tall. At the Grand Canyon's widest point, 76 Empire State Buildings would fit end to end. Write and solve an algebraic equation to the the width of the Grand Canyon at this point. Define a variable.

Define variable: w = width of grand canyon in meters

m/76 = 381

* 76 = * 76

m = 381 * 76

m = 28,956 meters

200

3x + 2 = 14

-2 = - 2

3x = 14 - 2

3x = 12

3x/3 = 12/3

x = 4

200

9 is the difference of a number n and 7.

9 = n - 7

+7 = +7

n = 16

300

45x = 180

/45 = /45

x = 4

300

3n = 15

/3 = /3

n = 15/3

n = 5

300

Millipedes have 4 legs per segment. The record number of legs on a millipede is 752. Write an algebraic equation and solve it for the number of leg segments the millipede has. Define the variable.

Define: s = number of leg segments

4s = 752

/4 = /4

s = 752/4

s = 188 leg segments

300

4f - 2 = 14

+ 2 = + 2

4f = 14 + 2

4f = 16

4f/4 = 16/4

f = 4

300

Solve: 15 - y = 8

15 - y = 8

+ y = + y

15 = 8 + y

- 8 = -8

7 = y

400

3.2x = 12.8

/3.2 = /3.2

x = 4

400

1/5 x = 30

1/5x = 30

* 5 = * 5

x = 30 * 5

x = 150

400

The area of Danielle's garden is one-twelfth the area of her entire yard. The area of the garden is 10 square feet. Find the area of the yard by writing an algebraic equation and solving for the area of the yard. Define the variable.

Define: a = area of the entire yard

1/12 a = 10

* 12 = * 12

a = 12 * 10

a = 120 sq. yards

400

x/5 - 1 = 2

x/5 = 2 + 1

x/5 = 3

x = 3 (5)

x = 15

400

On Saturday, you spend $33, give $15 to a friend, and receive $20 for mowing your neighbor’s lawn. You have $21 left. Write an algebraic equation to represent the amount you started with and solve. Define variable.

m = money you started with

m - 33 - 15 + 20 = 21

m - 48 + 20 = 21

m - 28=21

+28 = +28

m = $49

500

4/7x = 56

/4/7 = / 4/7

x = 56/1 * 7/4

x = 98

500

h/6.7 = 9.25

* 6.7 = * 6.7

h = 9.25 * 6.7

h = 61.975

500

DAILY DOUBLE

The height of the 50-milliliter beaker is one-third the height of the 2000-milliliter beaker. The height of the 50-milliliter beaker's height is 6 cm. Write an algebraic equation to find the height h (in centimeters ) of the 2000-milliliter beaker.

1/3h = 6

* 3 = *3

h = 18 cm.

500

x/2 - 4 = 6

+ 4 = +4

x/2 = 6 + 4

x/2 = 10

* 2 = * 2

2x = 10 (2)

x = 20

500

The drama club sold all the tickets for its annual production in three days. The club sold 143 tickets the first day and 295 tickets the second day. If the drama club sold 826 tickets, how many did it sell on the third day. Write an algebraic equation and solve for the number of tickets sold on the third day. Define the variable.

Define: t = number of tickets on 3rd day

143 + 295 + t = 826

438 + t = 826

- 438 = - 438

t = 826 - 438

t = 388 tickets