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4 years ago

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Solve and graph the absolute value inequality: |2x + 4| > 8. number line with open circles on negative 6 and 2, shading in be

tween. number line with closed circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 2 and 2, shading going in the opposite directions.

1 answer:

PolarNik [594]4 years ago

6 0

Answer:

Part 1) The solution of the absolute value is (-∞,-6)∪ (2,∞)

Number line with open circles on negative 6 and 2, shading going in the opposite directions

Part 2) The graph in the attached figure

Step-by-step explanation:

we have

$\left|2x+4\right|>8$

we know that

The absolute value has two solutions

step 1

<u><em>Find the positive case</em></u>

$+(2x+4)>8$

$2x>8-4$

$2x>4$

$x>2$

The solution is the interval ----> (2,∞)

All real numbers greater than 2

step 2

<u><em>Find the negative case</em></u>

$-(2x+4)>8$

Multiply by -1 both sides

$(2x+4)$

$2x$

$2x$

$x< -6$

The solution is the interval ----> (-∞,-6)

All real numbers less than -6

therefore

The solution of the absolute value is

(-∞,-6)∪ (2,∞)

Number line with open circles on negative 6 and 2, shading going in the opposite directions

step 3

using a graphing tool

see the attached figure

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