How do you solve and graph #4>=2y-5>=-2#?

Answer 1

#9/2>=y>=3/2#

To graph this, place solid dots over #9/2# and #3/2# (to indicate that both points are part of the solution) and connect the two points with a line segment.

When approaching a problem like this, we're actually doing two inequalities at the same time. What we do to the middle we must do to both sides:

#4 >= 2y-5 >= -2#

We can add 5 to all sides:

#4color(red)(+5) >= 2y-5color(red)(+5) >= -2color(red)(+5)#
#9>=2y>=3#

And now divide all sides by 2:

#9/color(red)(2)>=(2y)/color(red)(2)>=3/color(red)(2)#
#9/2>=y>=3/2#
To graph this, place solid dots over #9/2# and #3/2# (to indicate that both points are part of the solution) and connect the two points with a line segment.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To solve the compound inequality (4 \geq 2y - 5 \geq -2), first, add 5 to all parts of the inequality:

[4 + 5 \geq 2y - 5 + 5 \geq -2 + 5]

Simplify:

[9 \geq 2y \geq 3]

Then, divide all parts by 2:

[\frac{9}{2} \geq \frac{2y}{2} \geq \frac{3}{2}]

Which simplifies to:

[4.5 \geq y \geq 1.5]

So, the solution to the compound inequality is (4.5 \geq y \geq 1.5).

To graph it on a number line, draw a line with a closed circle at (y = 4.5) and another closed circle at (y = 1.5). Then shade the region in between the two points to represent the solution set.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7