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 solve a linear equation?

Back

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

Front

What is the first step in solving the equation 2(3x + 4) + 2 = 4 + 3x?

Back

The first step is to distribute the 2 on the left side: 6x + 8 + 2 = 4 + 3x.

Front

How do you isolate the variable in the equation 4x + 1 = 7x - 5?

Back

To isolate the variable, subtract 4x from both sides: 1 = 3x - 5, then add 5 to both sides: 6 = 3x, and finally divide by 3: x = 2.

Front

What is the solution to the equation 5y + 34 = -2(-7y + 1)?

Back

The solution is y = 4.

Front

How can you check if your solution to a linear equation is correct?

Back

You can check your solution by substituting the value back into the original equation to see if both sides are equal.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the term 'slope' refer to in a linear equation?

Back

The slope refers to the steepness of the line, calculated as the rise over run between two points on the line.

Front

What is the y-intercept in the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point where the line crosses the y-axis.

Front

How do you solve for x in the equation 7x + 5 + x - 3 + x = 5?

Back

Combine like terms to get 9x + 2 = 5, then subtract 2 from both sides: 9x = 3, and divide by 9: x = 1/3.