What is the solution to the inequality $- 10.5 - 7 x > - 4.5$ $-10.5 -7x> -4.5$ ?

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Answer 1 · 2016-05-18T03:03:04

$x < - \frac{6}{7}$ $x < -6/7$

Given,

$- 10.5 - 7 x > - 4.5$ $-10.5-7x > -4.5$

Start by adding $10.5$ $10.5$ to both sides.

$- 10.5 i + 10.5 - 7 x > - 4.5 i + 10.5$ $-10.5color(white)(i)color(red)(+10.5)-7x > -4.5color(white)(i)color(red)(+10.5)$

$- 7 x > 6$ $-7x > 6$

Divide both sides by $- 7$ $-7$ .

$\frac{- 7 x}{- 7} > \frac{6}{- 7}$ $color(red)((color(black)(-7x))/-7) > color(red)(color(black)6/-7)$

$x > - \frac{6}{7}$ $x > -6/7$

However, recall that you must always flip the inequality sign whenever you divide by a negative number. Thus,

$color(green)(|bar(ul(color(white)(a/a)color(black)(x < -6/7)color(white)(a/a)|)))$

What is the solution to the inequality -10.5 -7x> -4.5−10.5−7x>−4.5-10.5 -7x> -4.5?