Solve the following equations with fractions. x 4 − 2 3 = x 6 \frac{x}{4}-\frac23=\frac{x}{6}

Welcome to the practice. In this problem, we'd like to solve the equation x over four minus two thirds equals x over six. What makes this equation look a bit intimidating is that we have two fractions with an x in the numerator, x over four and x over six. So it doesn't really look like the one that we solved in the concept video. That means we should start by rewriting those two terms so that we can make the equation look a bit friendlier. So let's start with x over four. We know that x is equal to one x and that four is equal to four times one. So we can rewrite this as one x over four times one, which shows us how we can break up this fraction into one fourth times x over one. Now x over one is just x, so we can write this as one fourth x. And we can say that x over four is equal to one fourth x. We can do the same thing with x over six. Take a second, pause the video, follow the same steps, and you'll see that x over six is really just one sixth x. So we can rewrite this equation to be one fourth x minus two thirds is equal to one sixth x. And now we have it in the same form as the one that we solved in the concept video, so we're ready to follow our steps here to solve the equation, starting with step zero, which is clearing our fractions by multiplying by the least common denominator. So we wanna find the least common denominator of one fourth, minus two thirds, and one sixth. This means that we need to find the least common multiple of denominators four, three, and six, and that least common denominator is going to be 12. So let's multiply both sides of our equation by 12. That's gonna get us 12 times one fourth x minus two thirds is equal to 12 times one sixth x. And now we just need to distribute that 12. On the left, we end up getting 12 times one fourth x. Now, 12 times one fourth is three, so that's three x, and 12 times minus two thirds. 12 times two is 24, so this will get us minus 24 thirds. But because 24 divided by three is just eight, minus 24 thirds is really just minus eight. On the right side, we have 12 times one sixth x. Now 12 times one sixth is two, so this is just two x. Now we have no more fractions or decimals, so step zero is all set, and we would move on to step one. We don't have any parentheses or things we have to distribute, and we don't have any like terms on the left side or on the right side, so step one is all set, and we can move to step two, adding and subtracting to get variables on one side and constants on the other. We can see that our only constant is already on the left side, so let's keep constants on the left and move variables to the right. This means that we need to move this three x from the left, and we can get rid of it by subtracting three x from both sides of the equation. This is gonna cancel our three x on the left, leaving us with minus eight. And on the right, we get two x minus three x, which is minus x, or we can also think of it as minus one x. We're all set with step two, and now we can move on to step three using multiplication or division to isolate the variable. We wanna get rid of this minus one so we can divide both sides of the equation by minus one. And on the right, that's gonna cancel the minus one, just leaving us with x. And on the left, we get negative eight divided by negative one, which is just eight. So we end up getting that eight is equal to x. And that is step three all set. I encourage you to do step four and plug eight in for x back to the original equation to check your work. But once that's all set, you've solved the equation. Awesome job.

Table of contents

Skip topic navigation

1. Whole Numbers1h 55m

Multiplying Whole Numbers
46m

Dividing Whole Numbers
21m

Long Division
36m

Exponents
10m

2. Integers1h 7m

Introduction to Integers
16m

Multiplying Integers
24m

Exponential Expressions
10m

Dividing Integers
16m

3. Introduction to Solving Equations and Problem Solving43m

Simplifying Expressions
13m

Translating Word Phrases to Algebraic Expressions
6m

Introduction to Solving Equations
21m

Translating Sentences to Algebraic Equations
2m

4. Fractions1h 29m

Intro To Fractions and Mixed Numbers
44m

Simplifying Fractions
45m

5. Decimals1h 20m

Introduction To Decimals
27m

Rounding Decimals
12m

Adding And Subtracting Decimals
41m

6. Ratio, Proportion, and Percent2h 3m

Ratios and Rates
35m

Proportions
34m

Solving Percent Problems With Equations
16m

Applications of Percent
36m

7. Graphing and Introduction to Statistics40m

Tables
12m

Bar Graphs
3m

Frequency Distributions and Histograms
5m

Line Graphs
14m

Circle Graphs
4m

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement58m

US Units of Length
25m

Metric Units of Length
33m

10. Linear Equations and Inequalities6h 13m

The Distributive Property
17m

Review: Addition and Subtraction Properties of Equality
41m

Review: Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Introduction to Problem Solving
37m

Formulas
21m

Review: Percent Problem Solving
59m

Mixture Problem Solving
43m

Linear Inequalities in One Variable
46m

11. Graphing Linear Equations3h 17m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

12. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

13. Exponents and Polynomials3h 55m

Review: Evaluating Exponents
29m

The Product Rule
10m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

The Quotient Rule
13m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

14. Factoring Polynomials2h 42m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
20m

Sum & Difference of Cubes
12m

Quadratic Equations & Applications
41m

15. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying And Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

16. Relations and Functions2h 9m

Introduction to Relations and Functions
57m

Function Notation
15m

Graphing Common Functions
5m

Composition of Functions
24m

Direct & Inverse Variation
27m

17. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

18. Roots, Radicals, and Complex Numbers3h 57m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
47m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

19. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

20. Exponential and Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

21. Conic Sections and Systems of Nonlinear Equations2h 24m

Parabolas
35m

Graphing Circles
32m

Ellipses
35m

Hyperbolas
41m

22. Sequences, Series, and the Binomial Theorem1h 45m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

10. Linear Equations and Inequalities

Solving Linear Equations

Prealgebra, Beginning Algebra, & Intermediate Algebra

10. Linear Equations and Inequalities

Solving Linear Equations

Previous problemNext problem

Struggling with Prealgebra, Beginning Algebra, & Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Solve the following equations with fractions.
$\frac{x}{4} - \frac{2}{3} = \frac{x}{6}$

$x=$\frac$85$

$x=-8$

$x=8$

$x=-$\frac$85$

0 Comments

Previous problemNext problem

6:00m

Watch next

Master Solving Linear Equations with Fraction or Decimal Coefficients Example 1 with a bite sized video explanation from Patrick Ford

Struggling with Prealgebra, Beginning Algebra, & Intermediate Algebra?

Solve the following equations with fractions.x4−23=x6\(\frac{x}{4}\)-\(\frac\)23=\(\frac{x}{6}\)

Watch next

Solve the following equations with fractions.
$\frac{x}{4} - \frac{2}{3} = \frac{x}{6}$