# How do you solve and graph #x - 3< -7# or #x + 5>=8#?

graph{x<-4}

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To solve and graph the inequality ( x - 3 < -7 ) or ( x + 5 \geq 8 ), first, solve each inequality separately, then graph the solutions on a number line, and finally, combine the graphs.

For ( x - 3 < -7 ): [ x - 3 < -7 ] [ x < -7 + 3 ] [ x < -4 ]

For ( x + 5 \geq 8 ): [ x + 5 \geq 8 ] [ x \geq 8 - 5 ] [ x \geq 3 ]

Now, graph the solutions on a number line:

- For ( x - 3 < -7 ), the solution is ( x < -4 ), which is represented by an open circle at -4 and shading to the left.
- For ( x + 5 \geq 8 ), the solution is ( x \geq 3 ), which is represented by a closed circle at 3 and shading to the right.

Combining the graphs, the solution to ( x - 3 < -7 ) or ( x + 5 \geq 8 ) is ( x < -4 ) or ( x \geq 3 ), represented on the number line accordingly.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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