Solve the given linear equation. Check your solution. 2 ( x + 3 ) = 14 2\left(x+3\right)=14

this problem, we're asked to solve the given linear equation and then check our solution. The linear equation we're given here is two times x plus three equals 14. Now the very first thing we want to do here according to our steps is to simplify both sides of our equation by distributing anything that we need to into parentheses and combining any like terms. So let's do that here. I have this two that needs to get distributed to my x plus three. So distributing it to x gives me two times x, that's just two x, and then multiplying it by that three gives me six. So I have two x plus six equals 14. Now from here, we can move on to step two using our addition and subtraction properties of equality in order to collect all variable terms on one side and all constant terms on the other side. Now I only have one variable term, this two x, so I'm just gonna focus on my constants. Since my variable term is already over here on the left side of my equation, I'm gonna go ahead and move any constants over to the right. So I need to move that plus six over to the other side. Now in order to get that plus six to cancel over here, since it's being added, I can use subtraction. So subtracting six here using my subtraction property of equality to do this on both sides lets this cancel, leaving me with just two x. Then fourteen minuteus six will give me here eight. Then I have the equation two x equals eight and we're moving into step three, using our multiplication and division properties of equality to fully isolate our variable. Here, I just have this two multiplying by x. So in order to get rid of that multiplication to get that variable all by itself, I need to use division. So dividing by two on both sides leaves me with just x. And then I have eight divided by two, which will give me here four. So this gives me my solution here, x equals four. We have just one step left to follow here. That's checking our solution by plugging this back into our original equation. So putting four in for x to this equation, we get two times four plus three equals 14. We're checking, is this going to give us a true statement? So two times four plus three, four plus three will give me here seven. So I have two times seven. We're checking, is this equal to 14? Two times seven is 14, so I get the statement that 14 equals 14. This is definitely a true statement because these are the same exact value, so I know that I found my solution correctly, x equals four. Now there's actually another way that we could have gone about solving this linear equation. So I wanna walk you through that here as well because it may be useful to you as you continue on. Starting with our original equation, which was two times x plus three equals 14. According to our steps, we always want to start by simplifying both sides of our equation. And this will always work if we follow these steps in this order. But that's not to say that we could actually start with a slightly different step in solving this particular equation. Because we have only one instance of x and our ultimate goal here is to get that x all by itself, so we just wanna do whatever we can to get rid of anything else going on on that side of our equation, we could have actually started here by dividing out this two. So if I started here by dividing by two on both sides, whatever I do to one side I have to do to the other, those twos would cancel out, leaving me with just that x plus three. Then 14 divided by two would give me here seven. Then I could use my subtraction property of equality to subtract off three on both sides to get me that x equals seven minus three, which is four. Now this is the same exact answer that we got by following our steps. And again, these steps are a foolproof way to get a solution when working to solve a linear equation. But if you recognize early on that, hey, I could actually get rid of stuff slightly differently, Instead of following those steps exactly as written, I could go ahead and use my division property of equality because ultimately, we're just working to get our variable x all by itself. And dividing by two is one step that we could start with in order to do that. Now if you don't recognize that early on, that's totally okay. Remember, your steps will always work. And ultimately, no matter how you go about solving your linear equation, you should always always check your answer at the end by plugging it back into your original equation to ensure that you did it correctly. Feel free to let us know if you have any questions in the comments, 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
37m

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 Numbers2h 45m

Introduction to Radical Expressions
24m

Simplifying Radical Expressions
27m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
23m

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 Functions1h 5m

Introduction to Inverse Functions
25m

Exponential Functions
13m

Introduction to Logarithmic Functions
26m

14. Conic Sections & Systems of Nonlinear Equations58m

Graphing Circles
32m

Ellipses
15m

Parabolas
10m

15. Sequences, Series, and the Binomial Theorem1h 46m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

2. Linear Equations and Inequalities

Solving Linear Equations

Beginning & Intermediate Algebra

2. Linear Equations and Inequalities

Solving Linear Equations

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Multiple Choice

Solve the given linear equation. Check your solution.
$2 (x + 3) = 14$

$x=11$

$x=4$

$x=10$

$x=5.5$

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Verified step by step guidance

Start with the given equation: $2\left(x + 3\right) = 14$.

Apply the distributive property to remove the parentheses by multiplying 2 by each term inside the parentheses: $2 \times x + 2 \times 3$.

Rewrite the equation after distribution: \$2x + 6 = 14$.

Isolate the term with the variable by subtracting 6 from both sides: \$2x + 6 - 6 = 14 - 6$, which simplifies to $2x = 8$.

Solve for $x$ by dividing both sides by 2: $\frac{2x}{2} = \frac{8}{2}$, resulting in $x = 4$.

6:21m

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Struggling with Beginning & Intermediate Algebra?

Solve the given linear equation. Check your solution.2(x+3)=142\(\left\)(x+3\(\right\))=14

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Solve the given linear equation. Check your solution.
$2 (x + 3) = 14$