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Solve for xx and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (\varnothing∅), leave the number line blank.minus, 17, is less than or equal to, x, minus, 10, or, minus, 8, is greater than or equal to, x, minus, 10−17≤x−10or−8≥x−10

Question

Solve for xx and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (\varnothing∅), leave the number line blank.minus, 17, is less than or equal to, x, minus, 10, or, minus, 8, is greater than or equal to, x, minus, 10−17≤x−10or−8≥x−10

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Solution

The given inequalities are:

-17 ≤ x - 10 and -8 ≥ x - 10

Let's solve each inequality separately.

For -17 ≤ x - 10, add 10 to both sides to isolate x:

-17 + 10 ≤ x - 10 + 10

-7 ≤ x

So, x is greater than or equal to -7.

For -8 ≥ x - 10, add 10 to both sides to isolate x:

-8 + 10 ≥ x - 10 + 10

2 ≥ x

So, x is less than or equal to 2.

The solution to the system of inequalities is the intersection of the solutions to both inequalities. In this case, x is greater than or equal to -7 and less than or equal to 2.

So, the solution is -7 ≤ x ≤ 2.

On the number line, this would be represented by a closed circle at -7 and 2, with a line connecting them, indicating that all numbers between -7 and 2, inclusive, are solutions to the inequality.

This problem has been solved

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