To turn it into an equivalent function with no fractions, we have to multiply everything by a common factor. That will the number where if multiplied by 2, or 3, and then divided by 4, gives an integer. That'll be the LCF of the 3 numbers, which is 2 * 3 * 4 = 24. Let's do that now: [tex]24( \frac{2}{3}-1) = 24(\frac{3}{4}) [/tex]
Which simplifies to (form with no fractions): [tex]16x - 24 = 18[/tex]
To solve for x, we have to isolate it. So, let's add 24 to both sides: [tex]16x-24+24 = 18+24[/tex]
Which is: [tex]16x = 42[/tex]
Then, divide both sides by 16, to get: [tex]x = \frac{42}{16} = \frac{21}{8} [/tex]
