Simplify the following by combining like terms. 1 2 x + 3 4 x − 1 2 y + 1 2 y \frac12x+\frac34x-\frac12y+\frac12y

were asked to simplify the following by combining like terms. Now the algebraic expression we're given here is one half x plus three fourths x minus one half y plus one half y. Now looking to our steps here for simplifying algebraic expressions, the first thing we want to do is distribute any constants or variables into parentheses. Now looking at this particular expressions, there's nothing that needs to get distributed. So I can go ahead and move on to step two, which is to identify my like terms. Those terms that have the same variable raised to the same exponent. So looking at my expression here, my first term is one half x and my very next term is three fourths x. Both of these have that same variable x raised to the same exponent of one. Remember that exponent of one is implied when there is no exponent. So I have those two like terms and then next I have negative one half y and then positive one half y. These two terms have the same variable y raised to the same exponent again of one. So I've identified my like terms. Now let's move on to step three, grouping our like terms by writing them next to each other. Now in this particular expression, our like terms are already grouped. Those first two like terms are right next to each other, as are my second two. So moving on to our final step four, combining our like terms by adding or subtracting their coefficients. Now here, all of our coefficients are fractions. So we need to remember what we know about adding and subtracting fractions. Looking at these first two like terms, one half x plus three fourths x, these do not currently have the same denominator in the fraction. This first fraction has a two in the denominator and the second one has a four. So I need to give these common denominators, which I can easily do by taking that one half and multiplying it by two over two. So effectively just multiplying it by one. I'm not really changing its value. So one times two going across the top there is two. And then on the bottom, two times two is four. So with a like denominator, this becomes two fourths x. So I'm really taking two fourths x and adding it with three fourths x. So now I can go ahead and just add those coefficients by adding those fractions together. So since they have the same denominator, I can add those numerators. Two plus three gives me five. So five over four x. Now looking at my next two terms, I have a negative one half y and positive one half y. Now if I have negative one half and I add positive one half, those are going to actually cancel each other out and just give me a zero y. Now, I don't really need to write this zero y because zero times anything is just zero. So effectively this entire algebraic expression simplifies to just five fourths x. If you have any questions, feel free to let us know in the comments and let's keep going.

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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

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44m

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Set Operations and Compound Inequalities
42m

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38m

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39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

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Introduction to Relations and Functions
57m

Function Notation
15m

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5m

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24m

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27m

11. Roots, Radicals, and Complex Numbers3h 57m

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47m

Simplifying Radical Expressions
47m

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19m

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53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

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The Square Root Property
25m

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26m

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40m

Graphing Quadratic Equations
1h 28m

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Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

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Graphing Circles
32m

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35m

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35m

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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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Simplify the following by combining like terms.
$\frac{1}{2} x + \frac{3}{4} x - \frac{1}{2} y + \frac{1}{2} y$

$\frac{5}{4} y$

$\frac{5}{4} x - y$

$\frac{5}{4} y - x$

$\frac{5}{4} x$

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Problema precedenteProssimo problema

Guida verificata passo dopo passo

Identify the like terms in the expression $\frac12x + \frac34x - \frac12y + \frac12y$. Like terms are terms that have the same variable raised to the same power. Here, $\frac12x$ and $\frac34x$ are like terms, and $-\frac12y$ and $\frac12y$ are like terms.

Combine the $x$ terms by adding their coefficients: $\frac12 + \frac34$. Write this as $\left(\frac12 + \frac34\right)x$.

Combine the $y$ terms by adding their coefficients: $-\frac12 + \frac12$. Write this as $\left(-\frac12 + \frac12\right)y$.

Simplify the sums inside the parentheses to get the combined coefficients for $x$ and $y$. This will give you the simplified expression in terms of $x$ and $y$.

Write the final simplified expression by including only the terms with nonzero coefficients after combining like terms.