Solving Compound Inequalities

a

In order to isolate

y,

we can multiply both sides by

\text{-}5.

Since we're multiplying by a negative we need to flip the inequality sign.

\dfrac{y}{\text{-}5} \geq 5

MultNegIneqMultiply by

\text{-}5

and flip inequality sign

y \leq \text{-}25

The solution to the inequality is

y

-values less than or equal to

\text{-}25.

b

Let's start by multiplying both sides by $7.$ Then, we can collect all $x$ -terms on one side.

\text{-}3x \leq \dfrac{20-x}{7}

MultIneq

\text{LHS}\cdot 7 \leq \text{RHS} \cdot 7

\text{-}21x \leq 20-x

AddIneq

\text{LHS}+x\leq\text{RHS}+x

\text{-}20x \leq 20

DivNegIneqDivide by

\text{-}20

and flip inequality sign

x \geq \text{-}1

The solution to the inequality is all

x

-values greater than or equal to

\text{-}1.

c

Here we can subtract $3x$ and $8$ from both sides to simplify the inequality. Further, we'll divide both sides by $\text{-}10$ and remember to flip the inequality sign.

\text{-}7x+8 \gt 3x+16

SubIneq

\text{LHS}-3x\gt\text{RHS}-3x

\text{-}10x+8\gt 16

SubIneq

\text{LHS}-8\gt\text{RHS}-8

\text{-}10x\gt 8

DivNegIneqDivide by

\text{-}10

and flip inequality sign

x \lt \dfrac{8}{\text{-}10}

WriteDecWrite as a decimal

x \lt \text{-}0.8

$x \lt \text{-}0.8$ is the solution set of the inequality.

Solving Compound Inequalities 1.4 - Solution