16. Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does it mean to simplify an equation?

Back

Simplifying an equation means to combine like terms and reduce the equation to its simplest form.

Front

What is the first step in solving the equation 10x + 14 = 34?

Back

Subtract 14 from both sides to isolate the term with x.

Front

How do you combine like terms in an equation?

Back

You add or subtract the coefficients of the same variable. For example, 7x + 8x = 15x.

Front

What is the distributive property?

Back

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

Front

What is the solution to the equation 2x + 6 = 18?

Back

x = 6, found by subtracting 6 from both sides and then dividing by 2.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means to get the variable alone on one side of the equation.

Front

What is the correct way to distribute in the equation 2(3x + 4)?

Back

6x + 8, by multiplying 2 by both 3x and 4.

Front

What is a common mistake when solving linear equations?

Back

A common mistake is failing to combine like terms correctly.

Front

What is the purpose of checking your solution in an equation?

Back

To verify that the solution satisfies the original equation.