1/09/23 - Variables on Both Sides Warm-Up

Front

What is a variable in an equation?

Back

A variable is a symbol, often represented by a letter, that stands for an unknown value in an equation.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What is the first step in solving an equation with variables on both sides?

Back

The first step is to simplify both sides of the equation, if possible, and then move all terms involving the variable to one side.

Front

How do you combine like terms in an equation?

Back

You combine like terms by adding or subtracting the coefficients of terms that have the same variable raised to the same power.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.

Front

Solve for b: 2b + 8 − 5b + 3 = − 13 + 8b − 5

Back

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can satisfy the equation.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it can be written in the form ax + b = c, where a, b, and c are constants.

Front

Solve for c: 2c − 3 = 2(6 - c) + 7c

Back

c = -5.

Front

What is the significance of isolating the variable in an equation?

Back

Isolating the variable helps to find its value by getting it alone on one side of the equation.