How do you solve and graph the compound inequality #3x + 8 < 2# or #x + 12 > 2 - x#?

Answer 1

#3x+8 < 2# or #x+12 > 2 -x#
for all possible Real values of #x#.

Draw a solid number line or shade the entire Cartesian plane for the solution set of #x#

Given [1]#color(white)("XXXX")##3x+8 < 2# or [2]#color(white)("XXXX")##x+12 > 2 -x#
From [1] #color(white)("XXXX")##3x < -6# #color(white)("XXXX")##x < -2#
From [2] #color(white)("XXXX")##2x > -10# #color(white)("XXXX")##x > -5#
So the solution set for #x# all all values for which #color(white)("XXXX")##color(red)(x < -2)# or #color(blue)(x > -5)#
Any value that is not #< -2# will be #> -5# (and visa versa).
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Answer 2
To solve and graph the compound inequality 3x + 8 < 2 or x + 12 > 2 - x: 1. Solve each inequality separately. 2. Graph each solution set on the number line. 3. Combine the two graphs to get the solution for the compound inequality. For 3x + 8 < 2: Subtract 8 from both sides: 3x < -6 Divide both sides by 3: x < -2 For x + 12 > 2 - x: Add x to both sides: 2x + 12 > 2 Subtract 12 from both sides: 2x > -10 Divide both sides by 2: x > -5 Graph the solution sets for x < -2 and x > -5 on the number line. Combine both graphs to get the solution for the compound inequality.
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Answer from HIX Tutor

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.

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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