Algebra 1 Section 2.4

Definition An equation is a mathematical sentence stating that two expressions are equal.

Symmetric Property of Equality If a = b, then b = a.

Numerical Expressions …may be true …or false! 32 – 5(7) = -2(13) 9 – 35 = -26 -26 = -26 4(5) = 3 + 2(4) 20 = 3 + 8 20 = 11

An equation whose truth depends on the value of the variable Conditional Equation An equation whose truth depends on the value of the variable x + 4 = 7 If x = 3, it’s true! If x = 2, it’s false!

Definitions Each number that makes an equation true is called a solution of the equation. To solve an equation, you must find the values that make the equation true.

How would you solve these? x – 17 = -35 x + 10 = 142 x 5 = 21 3x = 9

Definitions An inverse operation is the operation that will reverse (undo) a given operation. Equivalent equations have the same solutions.

Addition Property of Equality If a = b and c is a real number, then a + c = b + c. You may also subtract the same number from both sides of an equation.

Multiplication Property of Equality If a = b and c is a real number, then ac = bc. You may also divide both sides of an equation by the same nonzero number.

To solve an equation… …find what is happening to the variable. Do the inverse operation on both sides.

Example 1 Solve x – 12 = 15. x – 12 = 15 x – 12 + 12 = 15 + 12 x = 27 Check: 27 – 12 = 15

Example 2 Solve x + = – . 2 3 7 12 x + – = – – 2 3 7 12 5 4 x = – 15

Example 2 Check: – + 5 4 2 3 – + 15 12 8 7 12 =

Example 4 Solve 3x = 99. 3x = 99 3x 3 = 99 x = 33

Solving Equations Determine the operation performed on the variable in the equation. Perform the inverse operation on both sides of the equation.

Solving Equations Simplify both sides of the equation. Check your answer.

Example 6 The difference of a number and 10 is 37. x 10 – = 37

Example 7 Solve the formula F = ma for a. F = ma F m = ma F m = a F m

Homework: pp. 66-68