Solve: 3 x+5=4(2 x-3)+7

Name: Problem 117, Chapter 3: Introductory Algebra for College Students
Uploaded: 2021-02-19T20:07:18-08:00
Duration: 4 min 1 s
Channel: Emily Stein
Description: Solve: 3 x+5=4(2 x-3)+7

Key Concepts

Linear Equations

Linear equations are algebraic expressions that equate two expressions with variables raised to the first power. They are solved by performing operations that simplify the equation and isolate the unknown variable, ensuring that the solution satisfies the equality.

Distributive Property

The distributive property allows you to multiply a single term by each term within a set of parentheses. This property is fundamental for simplifying expressions and equations, especially when dealing with terms that involve both variables and constants.

Combining Like Terms

Combining like terms involves consolidating terms in an equation that have the same variable part. This process simplifies expressions by summing coefficients, thereby making it easier to isolate the variable and solve the equation.

Isolating the Variable

Isolating the variable means rearranging the equation so that the variable appears by itself on one side of the equation. This process typically involves performing inverse operations such as addition, subtraction, multiplication, or division, enabling you to determine the variable's value.

Transcript

0:00 Welcome.

00:02 In this video, we're going to look at solving a basic linear equation.

00:06 Now, we know it's an equation because it has an equal sign in the middle.

00:10 So the goal, when we're dealing with an equation, is to determine what variable or what number we could plug in for the variable x that would make this true.

00:19 So we're going to make sure we use our order of operations.

00:23 Please excuse my dear aunt sally, or parentheses exponent, multiply, divide, add, subtract, all of those.

00:29 As well as distributing, combining like terms, and then our addition and multiplication properties of equality.

00:37 So i have here 3x plus 5 equals 4 times the quantity 2x minus 3 plus 7.

00:46 So the first thing i'm going to do when i'm dealing with an equation is i'll try and simplify anything i can on one side individually first.

00:54 So the left side of the equation, that's already very simplified.

00:57 On the right side, i'm going to distribute the four to both of the two terms in the parentheses.

01:03 And that gives me 8x.

01:05 4 times 2x is 8 minus 12.

01:09 And then we have plus 7.

01:10 The 4 does not distribute to the 7.

01:13 Here then we can add or combine like terms negative 12 plus 7.

01:22 That leaves me with 8x.

01:24 We have minus 5.

01:25 So i have 3x plus 5.

01:28 On the left equals 8x minus 5 on the right.

01:34 So at this point, we have simplified as much as we can on the right side of the equation, and we're going to start using our additive and multiplicative properties of equality in order to solve this.

01:46 So i'm going to choose to add the opposite or essentially subtract this negative 8x.

01:53 So on the right side, 8x minus 8x, that gives me 0.

01:58 And then on the left, 3x minus 8, 3 minus 8, that gives me negative 5x.

02:05 So i have negative 5x plus 5 is equal.

02:12 All we have over there is 0 minus 5 or negative 5...

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