Where Math Gets Real
Solving Inequalities An inequality compares quantities. Instead of an equal sign, inequalities are indicated by the symbols >, <, ≤ or ≥. Sometimes variables in inequalities have coefficients or are paired with another number. These inequalities require addition, subtraction, multiplication, or division to solve. You can use inverse operations to isolate and solve for the variable.
INEQUALITY
OPERATION
INVERSE OPERATION ISOLATING THE VARIABLE SOLUTION
b + 7 > 2 – 7 – 7
b + 7 > 2
addition
subtraction
b > -5
k – 6.2 ≤ 5.01 + 6.2 + 6.2
k – 6.2 ≤ 5.01
subtraction
addition
k ≤ 11.21
21 p 21
84 21
≥
p ≥ 4
21 p ≥ 84
multiplication
division
m ÷ 2.5 < -12 × 2.5 × 2.5
m ÷ 2.5 < -12
division
multiplication
m < -30
NOTE: If you have to multiply or divide by a negative number in order to isolate the variable, you will need to switch the direction of the sign.
less than
reater than or equal to
-4.25 s -4.25
14.45 -4.25
y ÷ -9 ≥ -6 × -9 × -9 y ≤ 54
< s > -3.4
reater than
less than or equal to
YOUR TURN ✎
4. g ÷ 7.2 > 8.5
1. h ÷ 24 ≤ 6
5. 126 ≥ -12 n
2. q + 7.3 > -13.2
6. 13.3 – z < 30
3. 2.4 d ≥ 23.4
These Drones Save Lives! > INVERSE OPERATIONS
Sessions 23 & 24 71
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