Answer:
[tex]p\geq -21[/tex]
Step-by-step explanation:
1. Simplify the expression
[tex]\frac{-1}{3}[/tex] · [tex](p+9)<=4[/tex]
Multiply the fractions:
[tex]\frac{(-1*(p+9))}{3} <=4[/tex]
Expand the parentheses:
[tex]\frac{(-p-9)}{3} <=4[/tex]
Break up the fraction:
[tex]\frac{-p}{3} +\frac{-9}{3} <=4[/tex]
Find the greatest common factor of the numerator and denominator:
[tex]\frac{-p}{3} +\frac{(-3*3)}{(1*3)} <=4[/tex]
Factor out and cancel the greatest common factor:
[tex]\frac{-p}{3} -3<=4[/tex]
2. Group all constants on the right side of the inequality
[tex]\frac{-p}{3} -3>=4[/tex]
Add 3 to both sides:
[tex]\frac{-p}{3} -3+3<=4+3[/tex]
Simplify the arithmetic:
[tex]\frac{-p}{3} <=4+3[/tex]
Simplify the arithmetic:
[tex]\frac{-p}{3}<=7[/tex]
3. Isolate the p
[tex]\frac{-p}{3} <=7[/tex]
Multiply to both sides by 3:
[tex]\frac{-p}{3} *3<=7*3[/tex]
Group like terms:
[tex]\frac{-1}{3} *3p<=7*3[/tex]
Simplify the left side:
[tex]-p<=7*3[/tex]
Simplify the arithmetic:
[tex]-p<=21[/tex]
4. Isolate the p
[tex]-p<=21[/tex]
Multiply both sides by-1:
When dividing or multiplying by a negative number, always flip the inequality sign:
[tex]-p*-1>=21*-1[/tex]
Remove the one(s):
[tex]p>=21*-1[/tex]
Simplify the arithmetic:
[tex]p>=-21[/tex]
5. Solution on a coordinate plane
Solution:
[tex]p\geq -21[/tex]
Interval notation:
[tex][-21, { \infty} ][/tex]
Terms and Topics:
Linear Equalities
