6 Steps for Solving Equations Step 1: Use the Distributive Property to remove the grouping symbols, () or Step 2: Simplify the expressions on each side of the equal sign “=” by combining like terms (variable and #’s)Step 3: Use the Addition and /or Subtraction Properties of Equality to get the variables on one side of the equal sign and the numbers without variables on the other side of the equals signStep 4: Simplify the expressions on each side of the equals sign by combining like termsStep 5: Use the Multiplication and/or Division Properties of Equalities to solve for the variable
7 Example 1 Method 1 Graphing means that the distance between b and –6 is 5 units. To find b on the number line, start at –6 and move 5 units in either direction.The distance from –6 to –11 is 5 units.The distance from –6 to –1 is 5 units.Answer: The solution set is
8 Example 1 cont Method 2 Compound Sentence Write as or Case 1 Case 2 Original inequalitySubtract 6 from each side.Simplify.Answer: The solution set is
9 Example 2Write an equation involving the absolute value for the graph.Find the point that is the same distance from –4 as the distance from 6. The midpoint between –4 and 6 is 1.The distance from 1 to –4 is 5 units.The distance from 1 to 6 is 5 units.So, an equation is .
10 Example 2 contAnswer:Check Substitute –4 and 6 into
11 Example 3 Then graph the solution set. Write as and Case 1 Case 2 Original inequalityAdd 3 to each side.Simplify.Answer: The solution set is
12 Example 4 Then graph the solution set. Write as or Case 1 Case 2 Original inequalityAdd 3 to each side.Simplify.Divide each side by 3.Simplify.Answer: The solution set is
13 Summary & Homework Summary: Homework: If |x| = n, then x = -n or x = n If |x| < n, then x = -n or x = n (inside)If |x| > n, then x = -n or x = n (outside)Homework:nonen-nn-nn-n