3x-2 over 2 (fraction format) -x over 4 (fraction format) = 15. I know that I need a LCD but when I tried 2 it didn't seem to work right. the only hint my math teache gave was the answer has to be a mixed number. Can anyone help?
(2x-2)/2 - x/4 = 15
LCD = 4
4x-4 -x = 60
3 x = 64
x = 64/3
To solve the equation (3x - 2)/2 - x/4 = 15, you'll need to find a common denominator (LCD) for the fractions involved.
Let's find the LCD for 2 and 4, which is 4.
Now, let's rewrite the equation using this common denominator:
[(3x - 2)(4)/(2)(4)] - [(x)(1)/(4)(1)] = 15
Simplifying this, we have:
[(12x - 8)/8] - (x/4) = 15
Multiply each term by 8 to eliminate the fractions:
8[(12x - 8)/8] - 8(x/4) = 8(15)
Cancel out the numerators and denominators:
12x - 8 - 2x = 120
Combine like terms:
10x - 8 = 120
Now, isolate the variable by adding 8 to both sides of the equation:
10x - 8 + 8 = 120 + 8
This simplifies to:
10x = 128
Finally, divide both sides by 10 to solve for x:
10x/10 = 128/10
x = 12.8
The solution to the equation (3x - 2)/2 - x/4 = 15 is x = 12.8. However, you mentioned that the answer should be in mixed number format. To convert the decimal into a mixed number, we'll divide the decimal part by the whole number part:
12.8 = 12 + 0.8
So, the mixed number format of the solution is 12 4/5.