Final answer:
To eliminate the fractions in the equation, you can multiply all the terms in the equation by the Least Common Denominator (LCD) of the fractions involved. In this case, the LCD would be 12. After multiplying, simplify the equation and solve for the variable x.
Step-by-step explanation:
To eliminate the fractions in the equation 7 - 3/4x + 2/3 = 1/2x - 6, we need to find a common denominator for the fractions.
To do this, we can multiply all the terms in the equation by the LCD (Least Common Denominator) of the fractions involved. In this case, the LCD would be 12, because it is the smallest number that both 4 and 3 divide into evenly.
So, we can multiply both sides of the equation by 12 to eliminate the fractions:
12*(7 - 3/4x) + 12*(2/3) = 12*(1/2x) - 12*6
This simplifies to: 84 - 9x + 8 = 6x - 72
From here, you can continue to solve the equation by combining like terms and isolating the variable x.