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How do you solve and graph #-23<=2x - 1<=1#?

Answer 1

Ethan Adkins

#-11 <= x <= 1#

Work out the two sides of the inequality separately:

#-23<=2x -1 <=1#

#-23<=2x -1 " and "2x -1 <=1# On the left, keep the x on the right. On the right keep it on the left.

#-23+1 <=2x " " 2x <= 1+1# #-" "22 <=2x " " 2x <=2# #" "-11 <= x " " x <= 1#

The two x terms are the same x, so combine them into one inequality:

#-11 <= x <= 1#

To graph it:

On a number line graph there will be a closed circle on -11 and a closed circle on 2, because both of these values are INCLUDED in the solution. Draw a line between the two circles to indicate that #x# can be any Real number between them.

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Answer 2

Avery Alexander

To solve and graph the compound inequality -23 ≤ 2x - 1 ≤ 1, follow these steps:

Add 1 to all parts of the inequality: -22 ≤ 2x ≤ 2
Divide all parts of the inequality by 2: -11 ≤ x ≤ 1
Draw a number line and mark the interval from -11 to 1, including both endpoints, since the inequality is inclusive.
Shade the interval between -11 and 1 to represent the solution set.

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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 and graph #-23&lt;=2x - 1&lt;=1#?

How do you solve and graph #-23<=2x - 1<=1#?