Which of the following are linear equations in one variable? a) -7 p=0 b) -2=5 g-4+g+10+3 g-1

Which of the following are linear equations in one variable?...

Key Concepts

Linear Equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable raised only to the first power. This means that there are no exponents on the variables, and no products of variables with each other. In a linear equation, the graph of the equation will be a straight line when plotted on a coordinate system.

One Variable Equation

A one variable equation involves only one unknown quantity and is typically expressed in the form of ax + b = 0, where a and b are constants. These types of equations can be solved uniquely by isolating the variable on one side to determine its value.

Combining Like Terms

Combining like terms is a fundamental process in algebra where terms that have the same variable parts are added or subtracted in order to simplify an expression. This step is essential in reducing equations to a standard form where the structure of the equation becomes clearer, and it facilitates easier solution of the equation.

Simplifying Expressions

Simplifying expressions involves using rules such as the distributive property, combining like terms, and performing arithmetic operations to rewrite an algebraic expression in its simplest form. This process is critical in identifying the type of equation, such as a linear equation in one variable, and in preparing the equation for solving.

Transcript

0:00 Hi everyone.

00:01 So we have these four equations and or expressions in front of us, and we want to know if they are linear equations in one variable.

00:11 A linear equation in one variable is simply an equation that could be written out in this form.

00:16 A, x plus b equals 0.

00:21 So in other words, we have the single variable here, the x, and we just have a constant out in front of it.

00:27 Notice how it's not to the second power or second.

00:30 Squared or anything.

00:31 It's just one single x.

00:36 Then we have a constant or added to a constant, so b, and then it's all set equal to zero.

00:44 Now another way to write this you might see is a x equals negative b, which we'll actually talk about in the second.

00:52 So let's start with a.

00:54 So is negative 7p equals zero a linear equation in one variable? and it is.

01:04 It doesn't look like it at first, but think of it like this.

01:08 So we have ax plus b equal zero for our form, right? so the x is p, but we'll leave it as x over here.

01:21 So a is equal to negative 7, right? and then our b is just simply zero.

01:27 And then the right hand side is already good because it's already set to zero.

01:30 So this meets the condition...

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