Combine like terms such that each variable only appears once. 3 4 x + 1 2 x \frac34x+\frac12x

Here we're asked to combine like terms such that each variable appears only once. Looking at our expression here, we have three fourths x plus one half x. Now, looking at these two terms, they both have a variable x with no exponent, which remember, implies having an exponent of one. So these are terms with the same variable raised to the same exponent, meaning they are like terms. So we can combine them by adding their coefficients. Now here, our coefficients are fractions, three fourths and one half. And they don't currently have the same denominator. So we need to make them have the same denominator so that we can add them together. Now looking at these two fractions, three fourths and one half, I can easily make one half have that same denominator of four by simply multiplying by two over two. So multiplying here, that gives me two over four. Now thinking about this logically, thinking about the fraction one half, if I were to ask you what is half of four, you would tell me two. So it makes sense that the fraction that we get here is then two fourths. So now that I've written this to have a like denominator or common denominator, this is three fourths x plus two fourths x, having written that equivalent fraction. So now I can add these like terms together by adding those coefficients three fourths plus two fourths. When adding fractions with like denominators, we can just add those numerators together. So three plus two gives me five, so this is five fourths x. So now we've combined our like terms such that our variable x appears only once. Let us know if you have questions and I'll see you in the next one.

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1. Review of Real Numbers2h 39m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
40m

2. Linear Equations and Inequalities3h 38m

The Addition and Subtraction Properties of Equality
41m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Linear Inequalities in One Variable
1h 11m

3. Solving Word Problems2h 43m

Introduction to Problem Solving
37m

Formulas
21m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphing Linear Equations in Two Variables3h 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

5. 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

6. Exponents and Polynomials3h 25m

The Product Rule
10m

The Quotient Rule
13m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

7. Factoring2h 42m

Factoring by Greatest Common Factor & Grouping
38m

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

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

Factoring Special Products
33m

Quadratic Equations & Applications
41m

8. 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

9. 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

10. 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

11. 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

12. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

13. Inverse, Exponential, & Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

14. Conic Sections & Systems of Nonlinear Equations2h 24m

Graphing Circles
32m

Ellipses
35m

Parabolas
35m

Hyperbolas
41m

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

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

1. Review of Real Numbers

Simplifying Expressions

Beginning & Intermediate Algebra

1. Review of Real Numbers

Simplifying Expressions

Problema precedenteProssimo problema

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Combine like terms such that each variable only appears once.
$\frac{3}{4} x + \frac{1}{2} x$

$\frac{4}{6} x$

$\frac{3}{8} x$

$\frac{5}{4} x$

$\frac{1}{4} x$

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Problema precedenteProssimo problema

Guida verificata passo dopo passo

Identify the like terms in the expression. Here, all terms have the variable $x$, so they can be combined by adding their coefficients.

Write down the coefficients of each term as fractions: $\frac{3}{4}$, $\frac{1}{2}$, $\frac{4}{6}$, and $\frac{3}{8}$.

Find a common denominator for all the fractions to add them easily. The denominators are 4, 2, 6, and 8. Determine the least common denominator (LCD).

Convert each fraction to an equivalent fraction with the LCD as the denominator, then add all the numerators together while keeping the common denominator.

Simplify the resulting fraction if possible, and then write the combined term as the simplified fraction multiplied by $x$.