• Add the same number to both sides.
• Subtract the same number from both sides.
• Multiply both sides by the same positive number.
• Divide both sides by the same positive number.
• Multiply both sides by the same negative number and reverse the sign.
• Divide both sides by the same negative number and reverse the sign.
Example:
Solve x + 7 < 15
Solution:
x + 7 < 15
x + 7 – 7 < 15 – 7
x < 8
Example :
Solve x – 6 > 14
Solution:
x – 6 > 14
x – 6+ 6 > 14 + 6
x > 20
Example :
Solve the inequality x – 3 + 2 < 10
Solution:
x – 3 + 2 < 10
x – 1 < 10
x – 1 + 1 < 10 + 1
x < 11
Example :
Solve the inequality 7 – x < 9
Solution:
7 – x < 9
7 – x – 7 < 9 – 7
– x < 2
x > –2 (remember to reverse the symbol when multiplying by –1)
Example :
Solve the inequality 12 > 18 – y
Solution:
12 > 18 – y
18 – y < 12
18 – y – 18 < 12 –18
– y < –6
y > 6 (remember to reverse the symbol when multiplying by –1)
Example:
Solve > 3
Solution:
> 3
× 5 > 3 × 5
x > 15
Example:
Solve
Solution:
If an equation has like terms, we simplify the equation and then solve it. We do the same when solving inequalities with like terms.
Example :
Evaluate 3x – 8 + 2x < 12
Solution:
3x – 8 + 2x < 12
3x + 2x < 12 + 8
5x < 20
x < 4
Example:
Evaluate 6x – 8 > x + 7
Solution:
6x – 8 > x + 7
6x – x > 7 + 8
5x > 15
x > 3
Example:
Evaluate 2(8 – p) ≤ 3(p + 7)
Solution:
2(8 – p) ≤ 3(p + 7)
16 – 2p ≤ 3p + 21
16 – 21 ≤ 3p + 2p
–5 ≤ 5p
–1 ≤ p
p ≥ –1 (a < b is equivalent to b > a)
An introduction to solving inequalities
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