Solving Multi-Step Equations

Two-Step Equations

100

2x - 3 = 5

x = 4

200

-0.5m - 0.75 = 2.15

m = -5.8

300

x/4 - 6 = 6

x = 48

400

(x + 6) / 4 = 4

x = 10

500

Jasmine’s cell phone company charges her $35 a month for phone service plus 0.50 for each text message. How many text messages does Jasmine send in a month if her bill was $52?

0.50x + 35 = 52

x = 34

34 text messages

Combine Like Terms Equations

100

5x + 3 − 2x = 3

x = 0 

200

5  = 2x − 25 + x

x = 10

300

4 + 4x - 5x = - 1

x = 5 

400

7 - 4x - 2x = - 35

x = 7 

500

- 10 + 2x - 4x = - 20 - 4

x = 7 

Distributive Property Equations

100

4(2x − 7) = −4

x = 3

200

2(2x + 6) =13

x = 0.25  or x = 1/4 

300

30 = −5(6x + 6)

x = -2

400

−4(8− 3x) =112

x = 12

500

-(28 - 4x) = -92

x = -16 

Area and Perimeter

100

Three sides of a triangle are side 1 = x + 5, side 2 = 2x - 3, side 3 = 3x + 4                                           The perimeter of the triangle is 60 units.                   Write and solve an equation to find x. 

x = 9

200

A rectangle has a width of 6 units and a length of 2x+8 units. If the area is 108, what is the value of x?

x = 5

300

A triangle has side lengths of 2x -3 feet, x + 4 feet, and 3x - 5 feet. The perimeter is 44 feet. Write and solve an equation to find x.

x = 8

400

A rectangle has a length of 2x + 5 units and a width of x + 2  units. Its perimeter is 50 units. Write and solve an equation to find x and each dimension.

x = 6   length = 17 units    width = 8 units

500

A triangle has a height of 3x + 1 units and a base of 10 units. The area is 95  square units. Write an equation for the area and solve to find x.

x = 6

Angle Relationships

100

Complementary Angles                                                      Angle 1 = 35                                                            Angle 2 = 4x+ 7                                            Find the value of x

x = 12

200

Supplementary Angles                                                      Angle 1 = 2x + 30                                                      Angle 2 = 2x - 10                                            Find the value of x

x = 40 

300

In a geometry class, Sarah is studying a pair of supplementary angles. The second angle is 6 more than 2 times the measure of the first angle. Write and solve an equation to find the measure of the larger angle.

Larger angle measures 122 degrees

400

For a set of complementary angles, the measure of the first angle is 15° less than 4 times the measure of the second angle.

Find the value of x.

x = 21

500

In an isosceles triangle, the two base angles are equal. The third angle (the top angle) is 10° less than 3 times the measure of one base angle.

If the sum of all three angles is 180°, find the measure of all three angles.

38, 38, and 104 degrees