solve for x
3x/4 - 21x/32 = 1 1/8
When adding fractions, they must all have the same denominator. Think of the denominator as the "unit" of measure. If you're counting eggs, you can't add the loose eggs and the cartons until you convert the cartons to eggs by multiplying by 12, since there are 12 eggs in each carton.
Similarly, you can't add 4ths and 32nds and 8ths unless you can make them all the same "unit."
Remember also that nothing changes when you multiply by 1. There are various ways of writing 1, and you can choose the way which gets you where you want to go.
3x/4 * 8/8 = 24x/32
1 1/8 = 9/8 * 4/4 = 36/32
Now we have everything as multiples of 1/32
24x/32 - 21x/32 = 36/32
3x/32 = 36/32
3x=36
x=12
^the answer is -12, it says so in the back of my book.
But once everything is multiples of 1/32, simplify.
then the problem should now be 24x-21x=-36 .
then subtract that, you get 3x=-36 .
-36/3=-12
therefore, your answer is x=-12.
Don't forget the negative.
To solve for x in the equation 3x/4 - 21x/32 = 1 1/8, we will follow these steps:
Step 1: Convert the mixed number 1 1/8 into an improper fraction.
- We have 1 + 1/8 = 8/8 + 1/8 = 9/8.
Step 2: Find a common denominator for the fractions on both sides of the equation. In this case, the smallest common denominator is 32.
Step 3: Rewrite the equation using the common denominator.
- The equation becomes:
(32 * 3x)/4 - (32 * 21x)/32 = (32 * 9)/8
Step 4: Simplify each term:
- On the left side, we simplify each term separately.
- (32 * 3x)/4 = 96x/4 = 24x
- (32 * 21x)/32 = 672x/32 = 21x
- On the right side, we multiply the numerator and denominator by 9.
- (32 * 9)/8 = 288/8 = 36
So the equation becomes:
24x - 21x = 36
Step 5: Combine like terms:
- 3x = 36
Step 6: Solve for x:
- Divide both sides of the equation by 3:
x = 36/3
Step 7: Simplify the fraction:
- 36 divided by 3 equals 12.
Therefore, the solution to the equation 3x/4 - 21x/32 = 1 1/8 is x = 12.