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Solve for xx and graph the solution on the number line below.minus, 13, is greater than, 2, x, minus, 5, or, 2, x, minus, 5, is greater than or equal to, 17−13>2x−5or2x−5≥17

Question

Solve for xx and graph the solution on the number line below.minus, 13, is greater than, 2, x, minus, 5, or, 2, x, minus, 5, is greater than or equal to, 17−13>2x−5or2x−5≥17

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Solution

Sure, let's solve these inequalities step by step:

  1. -13 > 2x - 5
  2. 2x - 5 ≥ 17

For the first inequality:

-13 > 2x - 5

Add 5 to both sides:

-13 + 5 > 2x

-8 > 2x

Divide both sides by 2:

-4 > x

So, x < -4

For the second inequality:

2x - 5 ≥ 17

Add 5 to both sides:

2x ≥ 22

Divide both sides by 2:

x ≥ 11

So, the solution to the inequalities is x < -4 or x ≥ 11.

To graph this on a number line, you would put an open circle at -4 and shade to the left (because x is less than -4), and you would put a closed circle at 11 and shade to the right (because x is greater than or equal to 11).

This problem has been solved

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