How do you solve the inequality #5x + 7 <2# and #5x + 7> –18#?

Answer 1

#-5 < x< -1#

This can be rewritten as

#-18<5x+7<2#

To solve this, isolate #x#. The first step will be subtracting #7#. However, subtract #7# from all parts of the inequality.

#-18-7<5x+7-7<2-7#

Which yields

#-25<5x< -5#

Now, divide each part by #5#.

#-5 < x< -1#

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Answer 2

Savannah Anderson

To solve the inequality 5x + 7 < 2 and 5x + 7 > -18, first subtract 7 from both sides of each inequality: For 5x + 7 < 2: 5x < -5 x < -1 For 5x + 7 > -18: 5x > -25 x > -5 Combining the results, the solution is: -5 < x < -1

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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.

How do you solve the inequality #5x + 7 &lt;2# and #5x + 7&gt; –18#?

How do you solve the inequality #5x + 7 <2# and #5x + 7> –18#?