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How do you solve and graph #y-2<4# and #y+4>7#?

Answer 1

Nathan Axel

#y > 3# and #y < 6#

#y - 2 < 4# and #y + 4 > 7#

So we kind of solve these inequalities like solving equations.

For #y - 2 < 4#, we add #2# to both sides like a normal equation:
#y < 6#

For #y + 4 > 7#, we subtract #4# to both sides:
#y > 3#

So we have to find the values that fulfill #y < 6# and #y > 3#.

This means any value between but not including #3 and 6#.

Here is the graph (It's easier to understand with a number line instead of a graph) but I did a graph. Where the red and blue intersect (or purple) is the solution:

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Answer 2

Hazel Anglin

To solve the inequality ( y - 2 < 4 ), you add 2 to both sides to isolate y, giving you ( y < 6 ). To solve the inequality ( y + 4 > 7 ), you subtract 4 from both sides to isolate y, giving you ( y > 3 ). So, the solution for the system of inequalities is ( 3 < y < 6 ). To graph this solution on a number line, you mark an open circle at 3 (since it's not included in the solution) and another open circle at 6. Then, draw a line connecting these two points.

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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&lt;4# and #y+4&gt;7#?

How do you solve and graph #y-2<4# and #y+4>7#?