How do you write an inequality and solve given "the sum of nine times a number and fifteen is less than or equal to the sum of twenty four and ten times the number"?

fythynwyrk0
2022-07-03
Answered

How do you write an inequality and solve given "the sum of nine times a number and fifteen is less than or equal to the sum of twenty four and ten times the number"?

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Immanuel Glenn

Answered 2022-07-04
Author has **12** answers

Step 1

Now that we know what our inequality is, we can now solve for x. To do this, we have to subtract 24 from each side:

$9x+15-24\le 24+10x-24$

$9x-9\le 10x$

Next, let's subtract 9x from each side:

$9x-9-9x\le 10x-9x$

$-9\le 9x$

Finally, let's divide each side by 9 to get our answer:

$-\frac{9}{9}\le \frac{9x}{9}$

$-1\le x$

Now that we know what our inequality is, we can now solve for x. To do this, we have to subtract 24 from each side:

$9x+15-24\le 24+10x-24$

$9x-9\le 10x$

Next, let's subtract 9x from each side:

$9x-9-9x\le 10x-9x$

$-9\le 9x$

Finally, let's divide each side by 9 to get our answer:

$-\frac{9}{9}\le \frac{9x}{9}$

$-1\le x$

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