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Solving Compound Inequalities

Solving Compound Inequalities 1.4 - Solution

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a
In order to isolate y,y, we can multiply both sides by -5.\text{-}5. Since we're multiplying by a negative we need to flip the inequality sign.
y-55\dfrac{y}{\text{-}5} \geq 5
y-25y \leq \text{-}25
The solution to the inequality is yy-values less than or equal to -25.\text{-}25.
b

Let's start by multiplying both sides by 7.7. Then, we can collect all xx-terms on one side.

-3x20x7\text{-}3x \leq \dfrac{20-x}{7}
-21x20x\text{-}21x \leq 20-x
-20x20\text{-}20x \leq 20
x-1x \geq \text{-}1
The solution to the inequality is all xx-values greater than or equal to -1.\text{-}1.
c

Here we can subtract 3x3x and 88 from both sides to simplify the inequality. Further, we'll divide both sides by -10\text{-}10 and remember to flip the inequality sign.

-7x+8>3x+16\text{-}7x+8 \gt 3x+16
-10x+8>16\text{-}10x+8\gt 16
-10x>8\text{-}10x\gt 8
x<8-10x \lt \dfrac{8}{\text{-}10}
x<-0.8x \lt \text{-}0.8

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