Solve the inequality.-
**C + 6 < –20**
(A.) c < –26
(B.) c < –14
(C.) c < 26
(D.) c < 14
**D/13≥ –3**
(A.) d ≥ –16
(B.) d ≥ 39
(C.) d ≥ 10
(D.) d ≥ –39
**–3p > –48**
(A.) p < 16
(B.) p > –51
(C.) p < –16
(D.) p > 16
c + 6 < ¨C 20 Subtract 6 to both sides
c < - 26
d /13 ¡Ý ¨C 3 Multiply both sides by 13
d ¡Ý - 39
¨C 3 p > ¨C 48 Divide both sides by - 3
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Remark :
The inequality sign reversed when you multiply or divide by a negative number.
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p < 16
A
D
A
c + 6 <= 20 Subtract 6 to both sides
c < - 26
d /13 > = 3 Multiply both sides by 13
d > = - 39
- 3 p > 48 Divide both sides by - 3
________________________________________
Remark :
The inequality sign reversed when you multiply or divide by a negative number.
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p < 16
To solve inequalities, we follow similar steps as we do for solving equations, with just one important difference.
For the inequality C + 6 < –20, we can solve it as follows:
1. Start by isolating the variable C by subtracting 6 from both sides of the inequality:
C < –20 - 6
C < –26
Therefore, the correct answer is (A.) C < –26.
For the inequality D/13 ≥ –3, we can solve it by multiplying both sides of the inequality by 13 (since the value is positive):
1. Start by multiplying both sides by 13:
13 * (D/13) ≥ –3 * 13
D ≥ –39
Therefore, the correct answer is (D.) D ≥ –39.
For the inequality –3p > –48, we can solve it by dividing both sides by -3 (since the coefficient of p is negative and we need to flip the inequality sign):
1. Start by dividing both sides by -3. Note that dividing by a negative number reverses the inequality sign:
(-3p)/(-3) < (-48)/(-3)
p < 16
Therefore, the correct answer is (A.) p < 16.