Question #ad414

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Question #ad414

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Answer 1 · 2017-12-03T23:05:01

$x \geq - 9$ $xge-9$

Explanation:

Let's start by turning this word problem into something easier to understand.

We will have $2$ $2$ ; it will be multiplied by some number plus $4$ $4$ .
We can write this as:
$2 (x + 4)$ $2(x+4)$

This product ( $2 (x + 4)$ $2(x+4)$ ) is "no more than," ( $\leq$ $le$ ) $3$ $3$ times that same number, added to $7$ $7$ . That will then have $4$ $4$ subtracted from it.
We can write this as:
$3 (x + 7) - 4$ $3(x+7)-4$

Here's our equation:

$2 (x + 4) \leq 3 (x + 7) - 4$ $2(x+4)le3(x+7)-4$

Multiply everything out and solve:

$2 x + 8 \leq 3 x + 21 - 4$ $2x+8le3x+21-4$

$2 x + 8 \leq 3 x + 17$ $2x+8le3x+17$

$2 x \leq 3 x + 9$ $2xle3x+9$

$- x \leq 9$ $-xle9$

$x \geq - 9$ $xge-9$

This last step is important: remember to flip the direction the inequality faces when dividing by a negative number!

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Question #ad414

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