Math CentralQuandaries & Queries


Question from Balkees, a student:


Hi Balkees,

I think your equation is

\[ \frac34 (4-8x) = 2x-\frac23 (6-12x)\]

If this is correct then I think it is the fractions that are causing you difficulty, so let's get rid of them. The fraction on the right side has a denominator of $3$ so multiply each side of the equation by $3.$ The result is

\[ 3 \times \frac34 (4-8x) = 3 \times \left(2x-\frac23 (6-12x)\right)\]

which simplifies to

\[ \frac94 (4-8x) = 3 \times 2x- 2 \times (6-12x)\]


\[ \frac94 (4-8x) = 6x- (12 - 24 x)\]

That's progress, one fraction is gone. Now multiply each side by $4.$ That will eliminate the second fraction.

Solve for $x.$

Write back if you need more assistance,

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