How do you solve $- \frac{2}{3} x - 4 < - 8 x - 2$ $-2/3x-4 < -8x-2$ ?

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Answer 1 · 2018-04-29T05:43:47

$x < \frac{3}{11}$ $x < 3/11$

$- \frac{2}{3} x - 4 < - 8 x - 2$ $-2/3x - 4 < -8x - 2$

First, add $4$ $4$ to both sides of the inequality:
$-2/3x - 4 quadcolor(red)(+quad4) < -8x - 2 quadcolor(red)(+quad4)$

$-2/3x < -8x + 2$

Add $8x$ to both sides of the inequality:
$-2/3x quadcolor(red)(+quad8x) < -8x + 2 quadcolor(red)(+quad8x)$

$7 1/3x < 2$

$22/3x < 2$

Multiply both sides by $3$ :
$22/3x color(red)(*quad3) < 2 color(red)(*quad3)$

$22/cancel(3)x cancel(color(red)(*quad3)) < 6$

$22x < 6$

$x < 6/22$

Divide numerator and denominator by $2$ :
$x < 6/22 color(red)(-: 2/2)$

$x < 3/11$

Hope this helps!

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