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2 Answers

Hi Melissa. As you may know, those vertical lines "|" are absolute value operators. If the the thing inside the absolute value marks is negative, then multiply it by -1 to make it positive. If the thing inside is positive, leave it as it is. For an equation like this, the absolute value marks mean there are two answers.

If 4y-3 ≥ 0, then the equation is

4y-3 = 4

If 4y-3 < 0, then the equation is

-(4y-3) =4

Let's solve these one at a time.

4y-3 = 4

Add 3 to both sides (what you do to one side of an equation, you must do to the other.)

4y-3 +3 = 4 +3

4y = 7

Divide both sides by 4:

4y/4 = 7/ 4

y = 7/4

Now let's solve the other equation, the one where we multiply everything inside the absolute value bars by -1.

-(4y-3) =4

Distribute the -1:

-4y + 3 = 4

Subtract 3 from both sides:

-4y + 3 -3 = 4 -3

-4y = 1

Divide both sides by -4:

-4y/-4 = 1/-4

y = -1/4

So the two answers are y = -1/4 and y = 7/4

If you plug either -1/4 or 7/4 into the original equation, it should make it true. This is how we check.

|4y-3|=4

|4(-1/4)-3|=4 AND |4(7/4)-3|=4

|-1-3|=4 AND |7-3|=4

|-4|=4 AND |4|=4

4 = 4 AND 4 = 4 CHECK!

Remember, an absolute value in an equation means at least 2 answers! For an equation like this where the power of x is 1 (no exponents), then there is exactly 2 answers.

the lines mean absolute value, so no matter if the soultion for 4y-3 is positive or negative it's absolute value is a positive 4

for now let's drop the lines and work it as a usual equation:
4y-3=4
add 3 to both sides
4y=7
divide both sides by 4
y=1.75
plug it back into original problem
|4(1.75)-3|=4
|7-3|=4
|4|=4


Hope this helps!