Solving Quadratic Equations using Factoring: Solving an equation with fractions

Worded problemsSolving the problemEquations with variables on both sidesOne sided equationsSolving an equation using all techniques
Question 1

Solve for x:

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

Question 2

Solve for X:

\( \frac{1}{2}(x+3)=0 \)

Question 3

Solve for X:

\( -\frac{1}{2}(x+\frac{1}{4})=\frac{1}{8} \)

Question 4

Solve for X:

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

Question 5

Solve for X:

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

Examples with solutions for Solving Quadratic Equations using Factoring: Solving an equation with fractions

Exercise #1

Solve for x:

−3(12x+4)=12 -3(\frac{1}{2}x+4)=\frac{1}{2}

Video Solution

Step-by-Step Solution

We open the parentheses on the left side by the distributive property and use the formula:

a(x+b)=ax+ab a(x+b)=ax+ab

−32x−12=12 -\frac{3}{2}x-12=\frac{1}{2}

We multiply all terms by 2 to get rid of the fractions:

−3x−12×2=1 -3x-12\times2=1

−3x−24=1 -3x-24=1

We will move the minus 24 to the right section and keep the corresponding sign:

−3x=24+1 -3x=24+1

−3x=25 -3x=25

Divide both sections by minus 3:

−3x−3=25−3 \frac{-3x}{-3}=\frac{25}{-3}

x=−253 x=-\frac{25}{3}

Answer

−253 -\frac{25}{3}

Exercise #2

Solve for X:

12(x+3)=0 \frac{1}{2}(x+3)=0

Video Solution

Answer

3-

Exercise #3

Solve for X:

−12(x+14)=18 -\frac{1}{2}(x+\frac{1}{4})=\frac{1}{8}

Video Solution

Answer

−12 -\frac{1}{2}

Exercise #4

Solve for X:

−14(x−2)=3 -\frac{1}{4}(x-2)=3

Video Solution

Answer

-10

Exercise #5

Solve for X:

14(x−8)=1 \frac{1}{4}(x-8)=1

Video Solution

Answer

12

Question 1

Solve for X:

\( -\frac{1}{2}(\frac{1}{4}x+\frac{1}{6})=\frac{1}{4}(\frac{1}{2}x+\frac{1}{3}) \)

Question 2

Solve for X:

\( \frac{1}{3}(\frac{1}{3}x+\frac{1}{6})=\frac{1}{18} \)

Question 3

Solve for X:

\( -\frac{1}{3}(\frac{1}{4}+\frac{1}{2}x)=\frac{1}{12} \)

Question 4

Solve for X:

\( \frac{1}{8}(\frac{1}{2}x-\frac{1}{3})=\frac{1}{4}(\frac{1}{4}x+\frac{1}{6}) \)

Question 5

Solve X:

\( -\frac{1}{6}(x+\frac{1}{3})=\frac{1}{2}(\frac{1}{3}x-\frac{1}{9}) \)

Exercise #6

Solve for X:

−12(14x+16)=14(12x+13) -\frac{1}{2}(\frac{1}{4}x+\frac{1}{6})=\frac{1}{4}(\frac{1}{2}x+\frac{1}{3})

Video Solution

Answer

−23 -\frac{2}{3}

Exercise #7

Solve for X:

13(13x+16)=118 \frac{1}{3}(\frac{1}{3}x+\frac{1}{6})=\frac{1}{18}

Video Solution

Answer

0

Exercise #8

Solve for X:

−13(14+12x)=112 -\frac{1}{3}(\frac{1}{4}+\frac{1}{2}x)=\frac{1}{12}

Video Solution

Answer

-1

Exercise #9

Solve for X:

18(12x−13)=14(14x+16) \frac{1}{8}(\frac{1}{2}x-\frac{1}{3})=\frac{1}{4}(\frac{1}{4}x+\frac{1}{6})

Video Solution

Answer

There is no solution

Exercise #10

Solve X:

−16(x+13)=12(13x−19) -\frac{1}{6}(x+\frac{1}{3})=\frac{1}{2}(\frac{1}{3}x-\frac{1}{9})

Video Solution

Answer

0