Solving Equations Using All Methods: Using fractions

Combining like termsDomain of definitionMonomialNumber of termsUsing additional geometric shapesDecimal numbersOpening parenthesesBinomialRearranging EquationsExercises with fractionsOne sided equationsAddition, subtraction, multiplication and divisionEquations with variables on both sides
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

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

Question 3

Find the value of the parameter X

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

Question 4

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

Question 5

Solve for X:

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

Examples with solutions for Solving Equations Using All Methods: 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

3x−19=89 3x-\frac{1}{9}=\frac{8}{9}

Video Solution

Answer

13 \frac{1}{3}

Exercise #3

Find the value of the parameter X

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

Video Solution

Answer

13 \frac{1}{3}

Exercise #4

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

Video Solution

Answer

32 \frac{3}{2}

Exercise #5

Solve for X:

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

Video Solution

Answer

4 4

Question 1

Find the value of the parameter X

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

Question 2

Find the value of the parameter X

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

Question 3

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

Question 4

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

Question 5

Solve for X:

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

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

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}

Exercise #8

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

Video Solution

Answer

−514 -\frac{5}{14}

Exercise #9

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

Video Solution

Answer

4027 \frac{40}{27}

Exercise #10

Solve for X:

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

Video Solution

Answer

7588 \frac{75}{88}