Siles 8Math - Solving Equations

Two-Step Equations

100

Write the equation to represent "Five more than twice a number is 15." Solve it.

Answers may vary.

5+2x=15

200

Solve the equation: 3x - 7 = 8.

x=5

300

If 2x + 5 = 17, what is the value of x?

x=6

400

Write and solve the equation for "The sum of a number and 12 equals 30."

x+12=30

x=18

500

A number decreased by 4 equals 10. Write the equation and find the number.

w-4=10

w=14

Multi-Step Equations

100

Solve: 2(x + 3) = 14.

x=4

200

What is x if 3(x - 2) + 4 = 10?

x=4

300

Solve the equation: 4x - 5 = 3x + 2.

x=7

400

If 5(2x - 1) = 20, what is x?

x=2.5

500

 Solve: 6 - 2(3x - 4) = 10.

x=2/3

Distributive Property

100

Simplify: 3(x + 4).

3x+12

200

Apply the distributive property to 5(2x + 3) and simplify.

10x+15

300

Expand and simplify: 2(3x - 5) + 4.

6x-6

400

Distribute and simplify: 7(x + 2) - 3(x - 4).

4x-26

500

If 4(a + 2) = 28, what is a?

a=5

Types of Solutions

100

What is a unique solution in an equation?

A unique solution in an equation is when there is only one possible value for the variable that makes the equation true.

200

Describe what it means for an equation to have no solution with an example.

An equation has no solution if there is no value for the variable that makes the equation true.

300

If an equation results in a true statement like 0 = 0, what type of solution does it have?

Infinity many solutions. 

400

Give an example of an equation with infinitely many solutions.

Answers may vary. 

500

Explain how you would determine the type of solution for the equation 2x + 6 = 2(x + 3).

Answers may vary. After distributing the 2 on the right side of the equation you have 2x+6=2x+6. If both side of the equation are the same then there are infinitely many solutions. 

Real World Application

100

A rectangle's length is twice its width. If the perimeter is 24, write and solve for the width.

w=4

200

If you save $50 a month, how many months will it take to save $300? Write the equation and solve.

50m=300

m=6

300

A car's value decreases by 15% each year. If it’s worth $20,000 now, how much will it be worth in one year? Write the equation and solve.

Equations may vary. 

Ex: c=0.85(20,000) or c=20,000-20,000(0.15)

c=17,000

400

Write and solve an equation for a situation where a student has $30 and spends $5 each week. How many weeks can they spend before running out?

Equations may vary. 

Ex. 30-5w=0

w=6

500

If a concert ticket costs $45 and you have $200, how many tickets can you buy? Write and solve the equation.

45x=200

x=4.444 (repeating)

You can buy 4 tickets with 20 dollars left over for a drink (and maybe a pretzel).