Inequality Vocabulary
A mathematical sentence that compares two expressions using symbols like >, <, ≥, or ≤.
An inequality
Twice a number plus 3 is greater than 11
2x + 3 > 11
x + 4 > 10
x > 6
Graph the solution: x > 3
Open circle on 3 with a line going right
You need more than 50 points to pass the level. Write and solve an inequality.
x > 50
The value that makes an inequality true when substituted for the variable.
A solution
Five less than 4 times a number is less than 19
4x - 5 < 19
3x - 5 < 16
x < 7
Graph the solution: x ≤ -2
Closed circle on -2 with a line going left
A concert ticket costs $25. You have $200. Write and solve an inequality to find the maximum number of tickets you can buy.
25x ≤ 200, so x ≤ 8
This symbol means “greater than or equal to.”
≥
One-third of a number plus 8 is greater than 10
1/3x + 8 > 10
-2x + 1 > -5
x < 3
Graph the solution to: x ≥ 0
Closed circle on 0 with a line going right
You earn $12 per hour and need to make more than $96. Write and solve an inequality.
12x > 96, so x > 8
This symbol means “less than."
<
The sum of a number and 7 is less than or equal to 25.
x + 7 ≤ 25
1/2x + 3 < 7
x < 8
Graph the solution: x < 4
Open circle on 4 with a line going left
You have $45 and want to buy snacks that cost $3 each. Write and solve an inequality to find how many you can buy.
3x ≤ 45, so x ≤ 15
What must you remember to do when multiplying or dividing both sides of an inequality by a negative number?
Reverse the inequality sign
Half a number minus 6 is greater than -3
1/2x - 6 > -3
4x - 9 > 3x + 2
x > 11
Graph the solution: x ≥ 1.5
Closed circle on 1.5 with a line going right
A taxi charges a $4 base fee plus $2 per mile. You have at most $20 to spend. Write and solve an inequality.
4 + 2x ≤ 20, so x ≤ 8