How do you solve $-2( x - 4) \leq - 10$ ?

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Answer 1 · 2016-12-29T17:45:02

$x >= 9$

First, expand the term within parenthesis by multiplying by the term outside the parenthesis:

$(color(red)(-2) * x) + (color(red)(-2) * -4) <= -10$

$-2x + (+8) <= - 10$

$-2x + 8 <= - 10$

Next we can subtract $color(red)(8)$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$-2x + 8 - color(red)(8) <= - 10 - color(red)(8)$

$-2x + 0 <= - 18$

$-2x <= -18$

New, we can solve for $x$ by dividing each side of the inequality by $color(blue)(-2)$ which will also keep the inequality balanced.

However, because this is an inequality and we are multiplying or dividing the inequality by a negative term we must also reverse the inequality:

$(-2x)/color(blue)(-2) color(red)(>=) (-18)/color(blue)(-2)$

$(color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(>=) 9$

$x >= 9$

How do you solve -2( x - 4) \leq - 10-2( x - 4) \leq - 10?