{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
{{ searchError }}
search
{{ courseTrack.displayTitle }}
{{ printedBook.courseTrack.name }} {{ printedBook.name }}

Solving Compound Inequalities

Solving Compound Inequalities 1.4 - Solution

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.
$\dfrac{y}{\text{-}5} \geq 5$
$y \leq \text{-}25$
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.

$\text{-}3x \leq \dfrac{20-x}{7}$
$\text{-}21x \leq 20-x$
$\text{-}20x \leq 20$
$x \geq \text{-}1$
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.

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

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