Question

What should be multiplied on both sides to solve the following equations 2/9x=3/4?

Answer 1

Answer:

By multiplying both sides of the equation by $\frac{4x}{3}$  we solve the equation.

Step-by-step explanation:

Given the equation:

$\frac{2}{9x} =\frac{3}{4}$

in order to solve for x, we need to bring the unknown "x" to the numerator. Such is normally done by first finding the so called "Least common Denominator" (LCD), and using it to multiply both sides of the equal sign to get rid of all denominators in the equation. This is similar in a way to the procedure of cross multiplication.

Notice that the LCD in our case is simply the straight product of all factors in the denominators : 9 * x * 4 = 36 x

$\frac{2}{9x} =\frac{3}{4}\\\frac{2}{9x} \,36\,x=\frac{3}{4}\,36\,x\\8=27\,x$

Then, in order to solve for the unknown "x" we need to isolate it on one side of the equal sign, so we need to divide both sides by the numerical factor 27 :

$x=\frac{8}{27}$

Therefore, if we want to make both operations we performed into a single process, what we actually did was multiply by 36 x and divide by 27:

$36\,x/27=\frac{36\,x}{27} =\frac{4x}{3}$

so we can say that we can achieve the solving of the equation in one step by multiplying both sides of the equal sign by " $\frac{4x}{3}$ " :

$\frac{2}{9x} =\frac{3}{4}\\\frac{2}{9x}\,\frac{4x}{3} =\frac{3}{4}\,\frac{4x}{3} \\\frac{8}{27} = x$