Solving Equations When do we use solving equations? We use solving equations methods when we know what the problem equals but not what the variable is. What rules do we need to follow: Do the opposite operation (inverse operations) of what is happening to the variable What you do to one side you must do to the other What are the steps: Draw the river Do the inverse operation Simplify Check your answer

Inverse Operations Operations that are the opposite of what is occurring: (they cancel each other out) x÷ ÷x

1) Solve r + 16 = 27 Think of this equation as a balance scale. Whatever you do to one side has to be done to the other to keep it balanced!

1) Solve r + 16 = 27 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of addition? Subtract 16

r = = 27 1) Solve r + 16 = Draw “the river” to separate the equation into 2 sides 2. Subtract 16 from both sides 3. Simplify vertically 4. Check your answer by substituting your answer back into the problem

2) Solve x + 2 = 43 Get the variable by itself. What is your first step? 1. Add 2 to both sides 2. Subtract 2 from both sides 3. Add 3 to both sides 4. Subtract 3 from both sides Answer Now

2) Solve x + 2 = Draw “the river” to separate the equation into 2 sides 2. Subtract 2 from both sides 3. Simplify vertically 4. Check your answer by substituting your answer back into the problem x = = 3 On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!

3) Solve 8 = m m = 5 2. m = m = m = 8/3 Answer Now

3) Solve 8 = m = m 8 = Draw “the river” to separate the equation into 2 sides 2.Add 3 to both sides 3.Simplify vertically 4.Check your answer by substituting your answer back into the problem