Translate Inequalities
What is the symbol for at most?
≤
Lisa is cooking muffins. The recipe calls for more than 7 cups of sugar. She has already put in 2 cups. How many more cups does she need to put in?
x + 2 > 7
x > 5
Lisa needs to put in more than 5 cups.
What is the symbol for at least?
≥
17 ≤ x
closed circle at 17, pointing right
After paying $5.00 for a salad, Taylor has no more than $27.00 left. How much money did she have before buying the salad?
x - 5 ≤ 27
x ≤ 32
Taylor had at most $32.
Three more than the product of -4 and a number is greater than 5
-4x + 3 > 5
4x > -24
x > -6
-5(x + 3) > -35
x < 4
-2x -12 < -4
x > -4, open circle at -4, pointing right
How many t-shirts can Banning buy with at least $40 if each t-shirt costs $8.00?
8x ≥ 40
x ≥ 5
Banning can buy at least 5 t-shirts.
The quotient of a number and 5 is no more than -35
x/5 ≤ -35
-3m ≤ 12
m ≥ -4
-2(x - 2) + 3x > -15
x > -19
-8x - 5 > 2x + 5
x < -1, open circle at -1, pointing left
Last Friday Marissa had $22.50. Over the weekend she received $6 per hour for cleaning. She now has over $82.50. How many hours did Marissa work?
6x + 22.50 >82.50
x > 10
Marissa worked for more than 10 hours.
5 more than a number, divided by -2, is at least -10
(5+x)/-2 ≥ -10
x/-2 < -3.4
x > 6.8
0.5(4x + 8) + 2x ≥ -3x + 18
x ≥ 2
-35 ≥ -2(x - 5) + 3
x ≥ 24, closed circle at 24, pointing right
Max's employer has at most $18.00 to spend on supplies for his crew. He buys gloves for $3.75, and he will use the rest of the money on tape measures. How many can he buy with if each tape measure costs $4.50?
4.5x + 3.75 ≤ 18
x ≤ 3.17
Max can only buy 3 tape measures.