Simplifying and Combining Like Terms: Solving an equation with fractions

Combining like termsUsing additional geometric shapesOne sided equationsOpening parenthesesExercises with fractionsSolving an equation using all techniquesEquations with variables on both sides
Question 1

Solve for x:

\( -\frac{1}{2}+\frac{1}{3}x=\frac{1}{5}+x \)

Question 2

Solve for x:

\( -\frac{1}{5}x+\frac{1}{4}x+\frac{1}{20}x-\frac{1}{5}=\frac{3}{10}-\frac{2}{5}+\frac{2}{10}x \)

Question 3

Solve for X:

\( \frac{1}{4}+\frac{2}{5}x=-\frac{3}{4}+\frac{1}{10}x \)

Question 4

Solve for X:

\( -\frac{1}{7}+\frac{3}{4}x=\frac{1}{8}x+\frac{3}{14} \)

Question 5

Solve for X:

\( \frac{1}{8}x+3=-\frac{1}{5}+\frac{5}{16}x \)

Examples with solutions for Simplifying and Combining Like Terms: Solving an equation with fractions

Exercise #1

Solve for x:

−12+13x=15+x -\frac{1}{2}+\frac{1}{3}x=\frac{1}{5}+x

Video Solution

Step-by-Step Solution

We will move the elements with the X to the left side and the elements without the X to the right side, changing the plus and minus signs accordingly.

First, we move the minus X to the left section:

−12+13x+x=15 -\frac{1}{2}+\frac{1}{3}x+x=\frac{1}{5}

Now we move the minus 1/2 to the right section:

13x+x=15+12 \frac{1}{3}x+x=\frac{1}{5}+\frac{1}{2}

We will find a common denominator for the fractions on the right side and reduce accordingly. Convert the mixed fraction on the left side into a simple fraction:

113x=2+510 1\frac{1}{3}x=\frac{2+5}{10}

43x=710 \frac{4}{3}x=\frac{7}{10}

Multiply by34 \frac{3}{4} to reduce the left side:

x=710×34=7×310×4=2140 x=\frac{7}{10}\times\frac{3}{4}=\frac{7\times3}{10\times4}=\frac{21}{40}

Answer

2140 \frac{21}{40}

Exercise #2

Solve for x:

−15x+14x+120x−15=310−25+210x -\frac{1}{5}x+\frac{1}{4}x+\frac{1}{20}x-\frac{1}{5}=\frac{3}{10}-\frac{2}{5}+\frac{2}{10}x

Video Solution

Step-by-Step Solution

  • Move similar terms to one side.

  • Create common denominators using the least common multiple of the different fractions.

  • Reduction of fractions.

Answer

-1

Exercise #3

Solve for X:

14+25x=−34+110x \frac{1}{4}+\frac{2}{5}x=-\frac{3}{4}+\frac{1}{10}x

Video Solution

Answer

−103 -\frac{10}{3}

Exercise #4

Solve for X:

−17+34x=18x+314 -\frac{1}{7}+\frac{3}{4}x=\frac{1}{8}x+\frac{3}{14}

Video Solution

Answer

814 \frac{8}{14}

Exercise #5

Solve for X:

18x+3=−15+516x \frac{1}{8}x+3=-\frac{1}{5}+\frac{5}{16}x

Video Solution

Answer

25615 \frac{256}{15}

Question 1

Solve for X:

\( -x+\frac{1}{4}-\frac{1}{3}+\frac{1}{8}=5+\frac{1}{4}x-\frac{1}{3}x \)

Question 2

Solve for X:

\( -\frac{1}{5}x+\frac{1}{3}-\frac{1}{4}x+1=3x-\frac{1}{5} \)

Question 3

Solve for X:

\( -\frac{1}{5}(x+\frac{1}{4})=\frac{7}{10}+\frac{3}{5}x-\frac{2}{5} \)

Question 4

Solve for X:

\( -\frac{1}{5}(x-\frac{1}{3})+\frac{1}{15}=-\frac{3}{5}x+\frac{1}{10} \)

Question 5

Solve for X:

\( -\frac{1}{5}(x+\frac{1}{5})+\frac{1}{3}=-\frac{1}{4}x+\frac{1}{5} \)

Exercise #6

Solve for X:

−x+14−13+18=5+14x−13x -x+\frac{1}{4}-\frac{1}{3}+\frac{1}{8}=5+\frac{1}{4}x-\frac{1}{3}x

Video Solution

Answer

−11922 -\frac{119}{22}

Exercise #7

Solve for X:

−15x+13−14x+1=3x−15 -\frac{1}{5}x+\frac{1}{3}-\frac{1}{4}x+1=3x-\frac{1}{5}

Video Solution

Answer

49 \frac{4}{9}

Exercise #8

Solve for X:

−15(x+14)=710+35x−25 -\frac{1}{5}(x+\frac{1}{4})=\frac{7}{10}+\frac{3}{5}x-\frac{2}{5}

Video Solution

Answer

−716 -\frac{7}{16}

Exercise #9

Solve for X:

−15(x−13)+115=−35x+110 -\frac{1}{5}(x-\frac{1}{3})+\frac{1}{15}=-\frac{3}{5}x+\frac{1}{10}

Video Solution

Answer

−112 -\frac{1}{12}

Exercise #10

Solve for X:

−15(x+15)+13=−14x+15 -\frac{1}{5}(x+\frac{1}{5})+\frac{1}{3}=-\frac{1}{4}x+\frac{1}{5}

Video Solution

Answer

−2815 -\frac{28}{15}