Which graph correctly represents x + 2y ≤ 4?

Graph is attached below

Step-by-step explanation:

First we replace inequality sign by = sign

x+ 2y = 4

Subtract x on both sides

divide by 2 on both sides

Make a table for graphing, plug in some numbers for x and find out y

x           y

-2         3

0           2

2          1

Now graph the table

For shading use test point (0,0)

 is true

So we shade the region that contains (0,0)

Presently: 2020

Let Kevin’s age be kevinPresentAge and Timothy’s age be timothyPresentAge for the present year 2020. The statement states that “Kevin is 6 years older than Timothy”

kevinPresentAge=timothyPresentAge+6

4 years ago: 2016

Let Kevin’s age be kevinOldAge and Timothy’s age be timothyOldAge for the old year of 2016. The statement states that “Kevin was twice as old as Timothy”

2. kevinOldAge=2∗timothyOldAge

Now we have two equations and we have to solve it simultaneously. But unfortunately, the variable names are not the same. kevinPresentAge is not the same as kevinOldAge . So what can be done?

The relationship between kevinOldAge and kevinPresentAge is the difference between the years. In the statement, it is given as 4 years ago, which is why I choose the year 2020 and 2016 for the explanation. Therefore:

3. kevinOldAge=kevinPresentAge−4

4. timothyOldAge=timothyPresentAge−4

So now, we substitute equation 3 and 4 into equation 2 and it would become:

2. kevinPresentAge−4=2∗(timothyPresentAge−4)

So now, we will solve equation 1 and 2 since they have the same variables. But before that, I’ll like to change the variable names to something more simple and mathematical. Let kevinPresentAge=x while timothyPresentAge=y . Please don’t ask me y I did that (just kidding). So the equation would now look like:

1. x=y+6

2. x−4=2∗(y−4)

There are a number of ways to solve simultaneous equation but let’s use substitution method. Substitute equation x in equation 1 into equation 2 and it would become:

y+6−4=2∗(y−4)

y+2=2y−8

2y−y=2+8

y=10

Now let’s go back to equation 1 with the solved y.

x=10+6

x=16

So there you have it.

x=kevinPresentAge=16

y=timothyPresentAge=10