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4 votes
Solve the inequality. Graph the solution.

-1/3 (p+9) ≤ 4

2 Answers

6 votes

Answer:


p\geq -21

Explanation:

1. Simplify the expression


(-1)/(3) ·
(p+9)<=4

Multiply the fractions:


((-1*(p+9)))/(3) <=4

Expand the parentheses:


((-p-9))/(3) <=4

Break up the fraction:


(-p)/(3) +(-9)/(3) <=4

Find the greatest common factor of the numerator and denominator:


(-p)/(3) +((-3*3))/((1*3)) <=4

Factor out and cancel the greatest common factor:


(-p)/(3) -3<=4

2. Group all constants on the right side of the inequality


(-p)/(3) -3>=4

Add 3 to both sides:


(-p)/(3) -3+3<=4+3

Simplify the arithmetic:


(-p)/(3) <=4+3

Simplify the arithmetic:


(-p)/(3)<=7

3. Isolate the p


(-p)/(3) <=7

Multiply to both sides by 3:


(-p)/(3) *3<=7*3

Group like terms:


(-1)/(3) *3p<=7*3

Simplify the left side:


-p<=7*3

Simplify the arithmetic:


-p<=21

4. Isolate the p


-p<=21

Multiply both sides by-1:

When dividing or multiplying by a negative number, always flip the inequality sign:


-p*-1>=21*-1

Remove the one(s):


p>=21*-1

Simplify the arithmetic:


p>=-21

5. Solution on a coordinate plane

Solution:


p\geq -21

Interval notation:


[-21, { \infty} ]

Terms and Topics:

Linear Equalities

User Kade
by
8.2k points
4 votes
Answer: p is greater than or equal to -21
Solve the inequality. Graph the solution. -1/3 (p+9) ≤ 4-example-1
User Matt Foley
by
8.1k points

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