How do you solve $2( x - 4) > 5x + 1$ ?

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Answer 1 · 2017-09-09T02:27:55

See a solution process below:

First, expand the terms in parenthesis by multiplying each term in the parenthesis by the term outside the parenthesis:

$color(red)(2)(x - 4) > 5x + 1$

$(color(red)(2) xx x) - (color(red)(2) xx 4) > 5x + 1$

$2x - 8 > 5x + 1$

Next, subtract $color(red)(2x)$ and $color(blue)(1)$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$-color(red)(2x) + 2x - 8 - color(blue)(1) > -color(red)(2x) + 5x + 1 - color(blue)(1)$

$0 - 9 > (-color(red)(2) + 5)x + 0$

$-9 > 3x$

Now, divide each side of the inequality by $color(red)(3)$ to solve for $x$ while keeping the inequality balanced:

$-9/color(red)(3) > (3x)/color(red)(3)$

$-3 > (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3))$

$-3 > x$

We can state the solution in terms of $x$ by reversing or "flipping" the entire inequality:

$x < -3$

How do you solve 2( x - 4) > 5x + 12( x - 4) > 5x + 1?