will you help me answer |4y-3|=4
will you help me solve
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
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.
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.
|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:
add 3 to both sides
divide both sides by 4
plug it back into original problem
Hope this helps!