Solving Equations by Multiplying or Dividing Both Sides by the Same Number

Find the value of X:

$3x=18$

We use the formula:

$a\cdot x=b$

$x=\frac{b}{a}$

Note that the coefficient of X is 3

Therefore, we will divide both sides by 3:

$\frac{3x}{3}=\frac{18}{3}$

We divide accordingly:

$x=6$

$6$

Find the value of the parameter X

$5x=\frac{3}{8}$

$ax=\frac{c}{b}$

$x=\frac{c}{b\cdot a}$

$\frac{3}{40}$

Find the value of the parameter X:

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

We use the formula:

$a\cdot x=b$

$x=\frac{b}{a}$

We multiply the numerator by X and write the exercise as follows:

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

We multiply by 4 to get rid of the fraction's denominator:

$4\times\frac{x}{4}=3\times4$

In the left section we will reduce the 4 and multiply the right section, we will obtain:

$x=12$

$12$

Find the value of the parameter X

$\frac{x+4}{3}=\frac{7}{8}$

First, we cross multiply:

$8\times(x+4)=3\times7$

We multiply the right section and open the parenthesis multiplying each of the terms by 8:

$8x+32=21$

We shift the sections, and remember to change the plus and minus signs accordingly:

$8x=21-32$Solve the subtraction exercise on the right side and divide by 8:

$8x=-11$

$\frac{8x}{8}=-\frac{11}{8}$

Convert the simple fraction into a mixed fraction:

$x=-1\frac{3}{8}$

$-1\frac{3}{8}$

Find the value of the parameter X:

$\frac{1}{8}x=\frac{3}{4}$

We use the formula:

$\frac{a}{b}x=\frac{c}{d}$

$x=\frac{bc}{ad}$

We multiply the numerator by X and write the exercise as follows:

$\frac{x}{8}=\frac{3}{4}$

We multiply both sides by 8 to eliminate the fraction's denominator:

$8\times\frac{x}{8}=\frac{3}{4}\times8$

On the left side, it seems that the 8 is reduced and the right section is multiplied:

$x=\frac{24}{4}=6$

$6$