Solving an Equation by Multiplication/ Division: Using fractions

Exercises on Both Sides (of the Equation)Combining like termsBinomialNumber of termsDecimal numbersRearranging EquationsUsing additional geometric shapesSolving an equation using all techniquesOne sided equationsSolving an equation with fractionsEquations with variables on both sidesAddition, subtraction, multiplication and division
Question 1

Find the value of the parameter X

\( \frac{1}{3}x+\frac{5}{6}=-\frac{1}{6} \)

Question 2

Find the value of the parameter X

\( \frac{1}{3}x=\frac{1}{9} \)

Question 3

Find the value of the parameter X

\( 3x-\frac{1}{9}=\frac{8}{9} \)

Question 4

Solve for X:

\( \frac{1}{6}x-\frac{1}{3}=\frac{1}{3} \)

Question 5

Solve for X:
\( \frac{2}{3}x-\frac{4}{6}=\frac{1}{3} \)

Examples with solutions for Solving an Equation by Multiplication/ Division: Using fractions

Exercise #1

Find the value of the parameter X

13x+56=−16 \frac{1}{3}x+\frac{5}{6}=-\frac{1}{6}

Video Solution

Step-by-Step Solution

First, we will arrange the equation so that we have variables on one side and numbers on the other side.

Therefore, we will move 56 \frac{5}{6} to the other side, and we will get

13x=−16−56 \frac{1}{3}x=-\frac{1}{6}-\frac{5}{6}

Note that the two fractions on the right side share the same denominator, so you can subtract them:

 13x=−66 \frac{1}{3}x=-\frac{6}{6}

Observe the minus sign on the right side!

 

13x=−1 \frac{1}{3}x=-1

 

Now, we will try to get rid of the denominator, we will do this by multiplying the entire exercise by the denominator (that is, all terms on both sides of the equation):

1x=−3 1x=-3

 x=−3 x=-3

Answer

-3

Exercise #2

Find the value of the parameter X

13x=19 \frac{1}{3}x=\frac{1}{9}

Video Solution

Answer

13 \frac{1}{3}

Exercise #3

Find the value of the parameter X

3x−19=89 3x-\frac{1}{9}=\frac{8}{9}

Video Solution

Answer

13 \frac{1}{3}

Exercise #4

Solve for X:

16x−13=13 \frac{1}{6}x-\frac{1}{3}=\frac{1}{3}

Video Solution

Answer

4 4

Exercise #5

Solve for X:
23x−46=13 \frac{2}{3}x-\frac{4}{6}=\frac{1}{3}

Video Solution

Answer

32 \frac{3}{2}

Question 1

Find the value of the parameter X

\( \frac{2}{3}x+\frac{1}{4}=\frac{3}{4} \)

Question 2

Solve for X:
\( \frac{4}{5}x+\frac{3}{7}=\frac{2}{14} \)

Question 3

Solve for X:
\( \frac{4}{9}+\frac{3}{5}x=\frac{4}{3} \)

Question 4

Solve for X:

\( \frac{9}{11}-\frac{8}{15}x=\frac{8}{22} \)

Question 5

Find the value of the parameter X

\( \frac{8}{3}-\frac{4}{5}x=-\frac{2}{10}x \)

Exercise #6

Find the value of the parameter X

23x+14=34 \frac{2}{3}x+\frac{1}{4}=\frac{3}{4}

Video Solution

Answer

34 \frac{3}{4}

Exercise #7

Solve for X:
45x+37=214 \frac{4}{5}x+\frac{3}{7}=\frac{2}{14}

Video Solution

Answer

−514 -\frac{5}{14}

Exercise #8

Solve for X:
49+35x=43 \frac{4}{9}+\frac{3}{5}x=\frac{4}{3}

Video Solution

Answer

4027 \frac{40}{27}

Exercise #9

Solve for X:

911−815x=822 \frac{9}{11}-\frac{8}{15}x=\frac{8}{22}

Video Solution

Answer

7588 \frac{75}{88}

Exercise #10

Find the value of the parameter X

83−45x=−210x \frac{8}{3}-\frac{4}{5}x=-\frac{2}{10}x

Video Solution

Answer

409 \frac{40}{9}

Question 1

\( \frac{-5+7x}{2}=22 \)

How much is Xworth?

Question 2

\( 12y+4y+5-3=2y \)

\( y=\text{?} \)

Exercise #11

−5+7x2=22 \frac{-5+7x}{2}=22

How much is Xworth?

Video Solution

Answer

7 7

Exercise #12

12y+4y+5−3=2y 12y+4y+5-3=2y

y=? y=\text{?}

Video Solution

Answer

−17 -\frac{1}{7}