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

πŸ†Practice solution of an equation by multiplying/dividing both sides

With this method, we can multiply or divide both sides of the equation by the same element without thereby altering the overall value of the equation. This means that the final result of the equation will not be affected because we have multiplied or divided both sides by the same element or number.Β 

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\( x+2x=9 \)

\( x=\text{?} \)

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Below, we provide you with some examples where we apply this method.

Example 1

3X=24 3X=24

We solve the equation and find the numerical value of X X by dividing both sides of the equation by the number 3 3 .

In this way, we neutralize and isolate the X X on the left side of the equation, while on the right side we obtain the result of the equation.

3X=24 3X=24 / :3 :3

X=8 X=8

The result of the equation is 8 8 .


Example 2

X2=5 \frac{X}{2}=5

We solve the equation and find the numerical value of X by multiplying both sides of the equation by the number 2. This way, we neutralize and isolate X on the left side of the equation, while on the right side we obtain the result of the equation.

X2=5 \frac{X}{2}=5 Β / Γ—2 \times2

X=10 X=10

The result of the equation is 10 10 .


Examples and exercises with solutions for solving equations by multiplying or dividing both sides by the same number

examples.example_title

Find the value of X:

3x=18 3x=18

examples.explanation_title

We use the formula:

aβ‹…x=b a\cdot x=b

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

Note that the coefficient of X is 3

Therefore, we will divide both sides by 3:

3x3=183 \frac{3x}{3}=\frac{18}{3}

We divide accordingly:

x=6 x=6

examples.solution_title

6 6

examples.example_title

Find the value of the parameter X

5x=38 5x=\frac{3}{8}

examples.explanation_title

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

x=cbβ‹…a x=\frac{c}{b\cdot a}

examples.solution_title

340 \frac{3}{40}

examples.example_title

Find the value of the parameter X:

x4=3 \frac{x}{4}=3

examples.explanation_title

We use the formula:

aβ‹…x=b a\cdot x=b

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

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

x4=3 \frac{x}{4}=3

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

4Γ—x4=3Γ—4 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 x=12

examples.solution_title

12 12

examples.example_title

Find the value of the parameter X

x+43=78 \frac{x+4}{3}=\frac{7}{8}

examples.explanation_title

First, we cross multiply:

8Γ—(x+4)=3Γ—7 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 8x+32=21

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

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

8x=βˆ’11 8x=-11

8x8=βˆ’118 \frac{8x}{8}=-\frac{11}{8}

Convert the simple fraction into a mixed fraction:

x=βˆ’138 x=-1\frac{3}{8}

examples.solution_title

βˆ’138 -1\frac{3}{8}

examples.example_title

Find the value of the parameter X:

18x=34 \frac{1}{8}x=\frac{3}{4}

examples.explanation_title

We use the formula:

abx=cd \frac{a}{b}x=\frac{c}{d}

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

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

x8=34 \frac{x}{8}=\frac{3}{4}

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

8Γ—x8=34Γ—8 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=244=6 x=\frac{24}{4}=6

examples.solution_title

6 6

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