Solving Equations using Addition and Subtraction.

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Presentation transcript:

Solving Equations using Addition and Subtraction

Inverse Operations What is an inverse? What is an inverse? Doing the opposite of what is given Doing the opposite of what is given EXAMPLE: Bob drove his garbage truck 8 miles. What’s the inverse? EXAMPLE: Bob drove his garbage truck 8 miles. What’s the inverse? Subtract 8 miles.Subtract 8 miles. Subtract 10. Subtract 10. Add 10Add 10 Subtract -2. Subtract -2. Add -2.Add miles -8 miles Inverses always get you back to zero! Subtract 10. (Add 10) = 0 Subtract -2. (Add -2). - (-2) + -2 = 0

Solve for x ! Jimmy has 12 cases of Pepsi in his car. Crazy Joe comes along and steals 5. How many cases does Jimmy have left? Jimmy has 12 cases of Pepsi in his car. Crazy Joe comes along and steals 5. How many cases does Jimmy have left? Crazy Joe Set up as an equation: = x = 7 X = 7 cases

Solve for x ! Crazy Joe continues to make his rounds and snags 8 cases of Dr. Pepper from Julie. Julie now only has 3 cases left. How many cases did she have to start with? Crazy Joe continues to make his rounds and snags 8 cases of Dr. Pepper from Julie. Julie now only has 3 cases left. How many cases did she have to start with? Set up as an equation: x - 8 = 3 (some number minus 8 = 3 ) x = 11 cases

Steps to Solve Equations! Step 1 Draw wall under the = Step 2 Get x by itself on one side of the wall. Move everything else away using the ‘inverse operation’. Step 3 Combine ‘like terms’ (simplify). Add or subtract numbers. Whatever you do to one side of the “wall” (= sign), you must do to the other!

Solve for x ! X – 10 = 5 X – 10 = x x x = 15 x = 15 Step 1 Draw wall under the = Step 2 Get x by itself on one side of the wall. Move everything else away. Take the inverse of – 10. Add to the other side. Step 3 Combine like terms (simplify) Whatever you do to one side of the “wall” (= sign), you must do to the other!

You Try! X – 3 = 10 X – 3 = 10 Step 1 Draw wall under the = Step 2 Get x by itself on one side of the wall. Move everything else away. Step 3 Combine like terms (simplify) x x x = 13 x = 13

Solve for x ! X + 3 = 25 Step 1 Draw wall under the = Step 2 Get x by itself on one side of the wall. Move everything else away. Step 3 Combine like terms (simplify) Watch your sign! x x x = 22 x = 22

Solve for x by simplifying first X - (-12) = 40 X - (-12) = 40 x x x x x x Step 1 Draw wall under the = Step 2 Simplify any numbers (usually negative signs) Step 3 Get x by itself on one side of the wall. Move everything else away. Step 4 Combine like terms (simplify) x = 28 x = 28

Solve for x by simplifying first X - 14 = - 17 X - 14 = - 17 x x x x Step 1 Draw wall under the = Step 2 Simplify any numbers (usually negative signs) Step 3 Get x by itself on one side of the wall. Move everything else away. Step 4 Combine like terms (simplify) x = - 3 x = - 3

Solve for x by simplifying first -33 = x = x x x Step 1 Draw wall under the = Step 2 Simplify any numbers (usually negative signs) Step 3 Get x by itself on one side of the wall. Move everything else away. Step 4 Combine like terms (simplify) x = - 41 x = - 41

Homework! Pg. 48 #12-20 Show your work! Otherwise, no credit!