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

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Answer 1 · 2017-02-26T20:14:21

$- 1 < x < 0$ $-1 < x < 0$

Given: $3 x - 5 < 2 x - 5 < 5 x - 2$ $" "3x-5<2x-5<5x-2" "$ Inequality(1)

Lets get rid of one of the $x$ $x$ terms

Subtract $2 x$ $2x$ from every part

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

Add $5$ $5$ to very part

$x < 0 < 3 x + 3 Inequality(2)$ $x<0<3x+3 " Inequality(2)"$
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$Observation(1): So x is negative and 3 x + 3 > 0$ $color(brown)("Observation(1): So "x" is negative and "3x+3>0)$

Investigate $3 x + 3 > 0$ $3x+3>0$

Factor out the 3

$3 (x + 1) > 0$ $3(x+1)>0$

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

$x + 1 > 0$ $x+1>0$

$x > - 1$ $x > -1" "$ Inequality(3)
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$Observation(2): Combining Inequality(3) with Inequality(2)$ $color(brown)("Observation(2): Combining Inequality(3) with Inequality(2)")$

$- 1 < x < 0$ $-1 < x < 0$

How do you solve 3x−5<2x−5<5x−23x-5 <2x-5 <5x-2?