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# Solving Compound Inequalities

## Solving Compound Inequalities 1.3 - Solution

a

Let's collect the $x$-terms on one side of the inequality with inverse operations.

$3-x\leq 2x-1$
$3\leq 3x-1$
$4\leq 3x$
$3x\geq 4$
$x\geq \dfrac{4}{3}$

$x\geq\frac{4}{3}$ solves the inequality. That is all $x$-values greater than or equal to $\frac{4}{3}.$

b

We solve this inequality similarly by collecting the $y$-terms on one side and the constants on the other.

$8y+6\gt 6y+2$
$2y+6\gt2$
$2y\gt\text{-}4$
$y\gt\text{-}2$

The solution to the inequality is $y\gt\text{-}2,$ meaning all $y$-values greater than $\text{-}2.$