Question

Solve the inequality. Graph the solution.

-1/3 (p+9) ≤ 4

Answer 1

`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

Answer 2

Answer: p is greater than or equal to -21