Question

Solve the inequality. Graph the solution. -1/3 (p+9) ≤ 4

Answer 1

Answer: p is greater than or equal to -21

Answer 2

Answer:

$p\geq -21$

Step-by-step explanation:

1. Simplify the expression

$\frac{-1}{3}$ · $(p+9)$

Multiply the fractions:

$\frac{(-1*(p+9))}{3}$

Expand the parentheses:

$\frac{(-p-9)}{3}$

Break up the fraction:

$\frac{-p}{3} +\frac{-9}{3}$

Find the greatest common factor of the numerator and denominator:

$\frac{-p}{3} +\frac{(-3*3)}{(1*3)}$

Factor out and cancel the greatest common factor:

$\frac{-p}{3} -3$

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

$\frac{-p}{3} -3>=4$

Add 3 to both sides:

$\frac{-p}{3} -3+3$

Simplify the arithmetic:

$\frac{-p}{3}$

Simplify the arithmetic:

$\frac{-p}{3}$

3. Isolate the p

$\frac{-p}{3}$

Multiply to both sides by 3:

$\frac{-p}{3} *3$

Group like terms:

$\frac{-1}{3} *3p$

Simplify the left side:

$-p$

Simplify the arithmetic:

$-p$

4. Isolate the p

$-p$

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