Solving Algebraic Equations Inverse Operations Two-Step & Multi-Step

Intro to Equations Equation - a mathematical sentence with an equal sign. It can be true, false, or open. An equation is true if the expression on both sides of the equal sign are equal. For example: 2 + 5 = 4 + 3 (TRUE) An equation is false if the expression on both sides of the equal sign are not equal. For example: 2 + 5 = 4 + 2 (FALSE)

Intro to Equations When you solve, you are finding the value of the variable (Variables include = n, t, m, s, x). You must find the value of the variable that will make both sides equal. An equation is considered open if it contains one or more variables. For example: x + 2 = 8 6 is a solution because when 6 is substituted in the equation for x, the equation is true.

Inverse Operations Inverse: opposite When we solve equations, you must perform inverse operations, meaning whatever you do to one side of the equation, you must do to the other side to keep the equation balanced. The inverse of adding is subtracting Additive inverses: 12 and -12 The inverse of multiplying is dividing Multiplicative inverses: 4 and ¼

Example of an Inverse Operation in an Equation Inverse Operations Example of an Inverse Operation in an Equation Solve x + 5 = 33 x + 5 – 5 = 33 – 5 Undo adding 5 by subtracting 5. x = 28 Simplify. This isolates x. Check x + 5 = 33 Check your solution in the original equation. 28 + 5 ? 33 33 = 33 Substitute 28 for x.

Write the inverse of each number Inverse Operations Write the inverse of each number + 20 – 18 -72 1/6 -16/1 + 15

Algebraic Equations Solve. y + 20 = 100 24 = a – 18 -72 = 9x 5z + 15 = 60