# How do you solve 3x-5 <2x-5 <5x-2?

Feb 26, 2017

$- 1 < x < 0$

#### Explanation:

Given: $\text{ "3x-5<2x-5<5x-2" }$ Inequality(1)

Lets get rid of one of the $x$ terms

Subtract $2 x$ from every part

$x - 5 < - 5 < 3 x - 2$

Add $5$ to very part

$x < 0 < 3 x + 3 \text{ Inequality(2)}$
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$\textcolor{b r o w n}{\text{Observation(1): So "x" is negative and } 3 x + 3 > 0}$

Investigate $3 x + 3 > 0$

Factor out the 3

$3 \left(x + 1\right) > 0$

Divide both sides by 3. Note that $\frac{0}{3} = 0$

$x + 1 > 0$

$x > - 1 \text{ }$Inequality(3)
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$\textcolor{b r o w n}{\text{Observation(2): Combining Inequality(3) with Inequality(2)}}$

$- 1 < x < 0$