Solving Equations Use your logic Warm Up What

What are equations and how do I solve them? An EQUATION is a mathematical

M+20 = 3 REMEMBER: what you do to one side, you must do to

Helpful hint! If the variable has two operation performed on it, try to add

Operation Inverse Mult. -2 Div. -2 Add 6 Subtract 6

Operation Inverse Div. 7 Mult. 7 Sub. 2 Add 2

Operation Inverse Add 11 Sub. 11 Div. 3 Mult 3

Extension Define a variable Set up an equation Solve the equation Answer the question

Warm Up: You Pick 6! (This will be collected)

Solving Multi-Step Solutions Do I have to distribute? Do I have to clean up?

Given Distribute Combine like terms (now a 2 -step) Combine x’s Combine constants

Given Distribute Combine like terms Combine x’s Combine constants Remove coefficients

One Solution (What we have been doing) If an equation has only one solution,

Infinite (or Many) Solutions If an equation has infinite solutions, any number will work

No Solution If an equation has no solutions, no number will work as an

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Solving Equations

Use your logic! (Warm Up)

What are equations and how do I solve them? An EQUATION is a mathematical statement containing an EQUAL SIGN claiming that two expressions are EQUAL. This means the “left side” & “right side” have the same value. A SOLUTION of an equation is any value for a variable that keeps the equation true. To CHECK, PLUG IN the variable. This means preform INVERSE OPERATIONS until the variable is on one side of the equation by itself. Addition and SUBTRACTING are inverses. Multiplication and DIVISION are also inverses.

M+20 = 3 REMEMBER: what you do to one side, you must do to the other

You try…

You try…

Helpful hint! If the variable has two operation performed on it, try to add or subtract first and multiply or divide last (exception = fractions)

Operation Inverse Mult. -2 Div. -2 Add 6 Subtract 6

Operation Inverse Div. 7 Mult. 7 Sub. 2 Add 2

You try …

Operation Inverse Add 11 Sub. 11 Div. 3 Mult 3

Extension Define a variable Set up an equation Solve the equation Answer the question

Warm Up: You Pick 6! (This will be collected)

Multistep Equations

Solving Multi-Step Solutions Do I have to distribute? Do I have to clean up? PICK ON THE LITTLE GUY (subtract the x with the smaller coefficient) Is the variable isolated? COMBINE LIKE TERMS (x with x, constant with constant) Do I have variables on both sides? MULTIPLY the number outside by each term inside ADD OR SUBTRACT any constants Is the variable multiplied? DIVIDE OR MULTIPLY too eliminate the coefficient

Given Distribute Combine like terms (now a 2 -step) Combine x’s Combine constants Remove coefficient

Given Distribute Combine like terms Combine x’s Combine constants Remove coefficients

You try…

Extension

Types of Solutions

One Solution (What we have been doing) If an equation has only one solution, no other numbers except that one solution will work in this equation

Infinite (or Many) Solutions If an equation has infinite solutions, any number will work as a solution. It doesn’t matter which number you pick! Every number you can think of will work as a solution when you check this equation.

No Solution If an equation has no solutions, no number will work as an answer to this equation. NO CHECK