Solving Linear Equations

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

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value of the variable (usually x) that makes the equation true.

Front

What is the first step in solving the equation 8x + 2 + 3x + 5 = x + 12?

Back

Combine like terms on the left side: 11x + 7 = x + 12.

Front

How do you isolate the variable in the equation 7 - 2(10x + 1) = 25?

Back

First, distribute the -2: 7 - 20x - 2 = 25, then combine like terms and isolate x.

Front

What is the solution to the equation 10 = 3x - 12?

Back

Add 12 to both sides to get 22 = 3x, then divide by 3 to find x = 22/3.

Front

What is the process to solve the equation 7x - 3x - 8 = 24?

Back

Combine like terms to get 4x - 8 = 24, then add 8 to both sides and divide by 4.

Front

What does it mean if a linear equation has no solution?

Back

It means that there is no value for the variable that can satisfy the equation, often resulting in a contradiction.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the rate of change of the dependent variable with respect to the independent variable in a linear relationship.

Front

How do you check your solution for a linear equation?

Back

Substitute the value of the variable back into the original equation to see if both sides are equal.

Front

What is the solution to the equation -4x = 24?

Back

Divide both sides by -4 to find x = -6.