Home > Algebra > Multi-Step Inequalities

How do you solve and graph #y - 2 > -3#?

Answer 1

#y > -1#
#color(white)("XXXX")#(see below for graphs)

Given an inequality, the following operations can be performed to both sides of the inequality without effecting the inequality relation:

Add any amount
Subtract any amount
Multiply by any amount #> 0#
Divided by any amount #> 0#

Given #y - 2 > -3#
We can add #2# to both sides, to get:
#color(white)("XXXX")##y > -1#

Since this is a relationship involving a single variable, it could be graphed on a number line (top image below); notice the hollow circle which indicates that the value #(-1)# is not included in the solution set.

You could also graph this relationship on the Cartesian plane (bottom image below); again, notice the broken line on the left indicates that #(-1)# is not to be included in the solution set.

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Answer 2

Eva Abramson

To solve the inequality (y - 2 > -3), you would add 2 to both sides to isolate (y). This gives you (y > -1). To graph this inequality, you would draw a dashed horizontal line at (y = -1) (since (y) is not equal to (-1)) and shade the region above the line.

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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 #y - 2 &gt; -3#?

How do you solve and graph #y - 2 > -3#?