Solving Multi-Step Equations & Inequalities

Solving Equations

100

5h + 2 + 2h = 23

h = 3

200

3b + b - 8 = 4

b = 3

300

If −5⁢x+7=−2⁢x−3, then x=

10/3 or 3.3 repeating

400

Alan has a business mowing lawns for $20 per lawn and raking leaves for $0.75 per pile. His goal is to earn exactly $30 each time he mows a lawn and rakes leaves. If x represents the number of piles of leaves, write an equation that  models Alan’s goal.

0.75x+20=30

500

The equation below is used to find C, the total cost for printing a quantity of books (b).

C=5⁢b+200

Which equation is equivalent equation solved for b?

b=(C-200)/5

Solving by Using the Distributive Property

100

2(x + 5) = 14

x = 2

200

5(d - 2) = 40

d = 10

300

7(4 - t) = -84

t = 16

400

What is the value of x if 15 – 2(x + 5) = 25?

x=-10

500

Solve.

6(y+3) - 2(y-6)=8

x=-5.5

Inequalities

100

Solve. 6p - 18 -2p ≤ -2

p ≤ 4

200

Solve. 2(6x - 5) < 14

x < 2

300

In the inequality below, let y represent the number of cakes a bakery makes each day.

2⁢y+20≤210

Which phrase most accurately describes the number of cakes the bakery makes each day?

• more than 95 cakes

• exactly 95 cakes

• at most 95 cakes

• less than 95 cakes

at most 95 cakes

400

If 21 more than 3 times a number is −15, what is the number?

-12

500

If x is an integer, what is the minimum value of x that satisfies the inequality?

-7(x-2)+1<x

2

Random

100

4x + 9 = 33

x = 6

200

Tallahassee’s largest taxi company charges $4.50 for the first mile and $2.50 for each additional mile. Raul hopes to make at least $50 from his first customer of the day.

2.50⁢m+4.50≥50

Using the inequality above, how many miles, m, after the first mile does Raul need to drive in order to make at least $50 in cab fare from his first customer?

m≥18.2

300

4(y - 2) + y = -13

y = -1

400

Tickets for a field trip cost $5 for students and $8 for adults. The total amount paid for tickets C can be found using the equation below, where s is the number of students who attend, and a is the number of adults.

C=5⁢s+8⁢a

Which equation is equivalent when solved for s 

s= (C-8a)/5

500

If the sum of three consecutive even integers is  216, what is the largest of these integers?

74

Word Problems

100

WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?

n - Julie's sister's age n + 3 = 11 n = 8 Julie's sister is 8 years old.

200

Bella earns $7.50 per hour on the weekends babysitting. How many hours will she need to babysit to earn at least $120?

x ≥ 16

300

Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?

b = 28

400

Mr. Bucci goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a bag of raisins?

r - cost of a bag of raisins 17r + 2.97 = 34.76 r = 1.87 Each bag of raisins cost $1.87

500

Dylan has $100. He wants to buy a book for $20 and some CDs for $15 each. At most, how many CDs can Dylan buy?

C = 5 (Interpret the quotient)