Solving Linear Equations and Errors

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

How do you isolate a variable in a linear equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side. For example, to solve x + 5 = 10, subtract 5 from both sides to get x = 5.

Front

What does it mean to solve an equation?

Back

Solving an equation means finding the value(s) of the variable(s) that make the equation true.

Front

What is the first step in solving the equation -81 = -35 - p?

Back

Add p to both sides and add 81 to both sides to isolate p.

Front

Solve the equation -20 = 5(x + 2).

Back

x = -6.

Front

What is the solution to the equation x + 12 = 20?

Back

x = 8.

Front

Identify the error in the following steps: -3(x + 2) = -2(2x - 4) leads to -6x - 6 = -4x + 8. What is wrong?

Back

The error is in step 2, where the distribution was incorrectly applied.

Front

What is the solution to the equation -5x + 1 = -19?

Back

x = 4.

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 two or more terms inside a set of parentheses.

Front

What is an inverse operation?

Back

An inverse operation is an operation that reverses the effect of another operation. For example, addition and subtraction are inverse operations.