Solving Equations and Inequalities

Front

What is the general form of a linear equation in two variables?

Back

The general form of a linear equation in two variables is Ax + By = C, where A, B, and C are constants.

Front

How do you solve for y in the equation 8x + 4y = 16?

Back

To solve for y, rearrange the equation to isolate y: 4y = 16 - 8x, then divide by 4: y = -2x + 4.

Front

What does the inequality symbol '>' indicate?

Back

The symbol '>' indicates that the value on the left is greater than the value on the right.

Front

What is the solution to the equation x + 7 = 28?

Back

The solution is x = 21.

Front

When graphing an inequality, what does an open circle represent?

Back

An open circle represents that the endpoint is not included in the solution set, used with < or >.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows the relationship between expressions that are not necessarily equal.

Front

How do you graph the inequality x < 5?

Back

To graph x < 5, draw a number line, place an open circle at 5, and shade to the left to indicate all values less than 5.

Front

What is the solution set of the inequality 6 > x?

Back

The solution set is all real numbers less than 6.

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

How do you determine if a point (x, y) is a solution to an equation?

Back

Substitute the x and y values into the equation. If the equation holds true, then the point is a solution.