Writing Inequalities from Word Problems
Write an inequality: "A number plus 7 is at least 15."
x+7≥15
Solve: x-4>9
x>13
Solve: 2x+5≤15
x≤5
Graph x>−3 on a number line.
Open circle at -3, shade to the right.
A video game needs a minimum score of 50 points to advance. Write an inequality.
s≥50
"Maria has less than $20 to spend on snacks." Write an inequality.
s<20
Solve: x+6≤10
x≤4
Solve: 3x−4>11
x>5
Graph x≤4 on a number line.
Closed circle at 4, shade to the left.
A school club can have no more than 30 members. Write an inequality.
m≤30
"The temperature is no more than 32°F." Write an inequality.
t≤32
Solve: x/5≥3
x≥15
Solve: 2x−7≥9
x≥8
Graph x≥−1 on a number line.
Closed circle at -1, shade to the right.
Sarah earns $12 per hour and wants to earn at least $60. Write and solve an inequality.
12h≥60; h≥5
"A student must read at least 50 pages to complete the assignment." Write an inequality.
p≥50
Solve: -2x<8
x>−4 (flip the sign when dividing by negative)
Solve: x/4+3<7
x<16
Graph -5<x<2 on a number line.
Open circle at -5, open circle at 2, shade between.
A car rental costs $25 plus $0.50 per mile. You have at most $100 to spend. Write an inequality.
25+0.5m≤100
"The number of tickets sold (t) must be between 100 and 250 inclusive." Write an inequality.
100≤t≤250
Solve: 7+x<2
x<-5
Solve: 5x−2≤3x+10
x≤6
Graph x≤−2 or x>3 on a number line.
Closed circle at -2 shade left, or open circle at 3 shade right.
A bakery can bake between 200 and 500 cupcakes per week. Write a compound inequality and graph it.
200≤c≤500