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 (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 7x = 3x + 24?

Back

Subtract 3x from both sides to get 4x = 24, then divide by 4 to find x = 6.

Front

What is the solution to the equation 3(5x + 10) + 10 = 6x - (x + 10)?

Back

The solution is x = -5.

Front

How do you check if x = 1/2 is a solution for the equation 8x + 2 + 3x + 5 = x + 12?

Back

Substitute x = 1/2 into the equation: 8(1/2) + 2 + 3(1/2) + 5 = 1/2 + 12. Both sides equal 12, so it is a solution.

Front

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

Back

The slope indicates the steepness of the line and the direction it goes. A positive slope means the line rises, while a negative slope means it falls.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept is the value of y when x = 0, represented by b in the equation.

Front

How do you set up an equation to compare Joe’s Canoes and Callie’s Canoes charges?

Back

Set up the equation: 20 + 4h = 14h, where h is the number of hours.

Front

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

Back

The solution is x = 22/3.