One Step Equations Review

An equation is a mathematical sentence that contains an equal sign. If an equation contains variables, a value for the variable that makes the equation true is a solution to the equation. To test if a value is a solution of an equation, substitute the value for the variable.

To solve equations, you have to perform inverse operations to get the variable by itself. Remember- addition and subtraction are inverse operations. If an equation contains addition, solve it by subtracting from both sides to undo the addition. Similarly, if an equation contains subtraction, solve it by adding to both sides to undo the subtraction.

Multiplication and division are inverse operations. If an equation contains multiplication, solve it by dividing both sides to undo the multiplication. Similarly, if an equation contains division, solve it by multiplying both sides to undo the division.

An inequality is a statement that two quantities are not equal. Inequalities may contain a variable. The same properties that are used to solve equations are used to solve inequalities. Values of the variable that make the inequality true are solutions to the inequality.

We will graph the solutions on a number line.

If the inequality is < or >, you'll use an open circle to mark the number portion of the inequality.
If it is ≤ or ≥ then you'll use a closed circle.

When two quantities have a constant (unchanged) ratio, their relationship is known as direct variation. Many individuals say that one variable "varies directly" as the other. The constant ratio is called the constant of variation. A direct variation relationship can be represented by a linear equation in the form y = kx, where k is called the constant of proportionality (or constant of variation).

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