Solving Equations The art of balancing values

Words to Know Constant Coefficient Like Terms Variable Evaluate Justify Viable

What is the difference between an equation and an expression? an expression is a phrase without an equal sign. This means that the variable in an expression can be changed and the expression can be evaluated differently. An equation has an equal sign. Therefore one side of an equation is equal to a value on the other side.

Now, let's examine how to write equations. The same key words that helped you write expressions may also help you write equations. Here are some additional key words that you may find helpful. Key Words for Addition or Multiplication Equations how many all together how many in all how many total Key Words for Subtraction Equation how many more how many fewer how many left how much change

4 times a number is twelve. First, notice that we have the word “times” which means to multiply. We also have the word “is” which is a key word for equal. So the equation is 4x = 12 But we still don’t know what the number is.

Simplifying an expression is like wrapping a present using the order of operations to put it all together. Wrapping a present Put the present in a box Wrap paper around box Tape the paper closed Tie a ribbon around it Simplifying expression Do what is inside the parenthesis Simplify Exponents Multiply and Divide from left to right Add and Subtract from left to right

Solving Equations is like unwrapping the present using the reverse order of operations and inverse operations Unwrapping a present Untie ribbon Undo tape Remove wrapping paper Take present out of box Solving Equations Subtract to get rid of Addition and Add to get rid of subtraction Multiply to get rid of Division and Divide to get rid of Multiplication Use roots to get rid of exponents Undo the work inside grouping symbols using this same order.

So let’s try it WorkJustification 4x = 12given equation 4x /4 = 12/4Division Property of Equality 1x = 3Substitution Property We see that the coefficient is four, meaning the variable is multiplied by four. To get rid of this we need to do the inverse operation which is: We must divide both sides by four to keep both sides equal, Just like keeping a scale balanced Whenever, you substitute any part of an equation with an equivalent value it is called the Substitution Property, so we replace 4/4 with 1 and 12/4 with 3 X = 3Multiplicative Identity Property One times the value of x equals x

Properties you need to know Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Substitution Property Additive Identity Property Multiplicative Identity Property Multiplicative Inverse Property Symmetric Property of Equality

Your Turn Seven less than a number is fourteen. WorkJustification X – 7 = 14given equation X – = Addition Property of Equality X + 0 = 21Substitution Property X = 21Additive Identity Property

Your Turn WorkJustification m = 3given equation m = 3Commutative Property of Addition m – (-12) = 3 – (-12) Subtraction Property of Equality m = Subtraction of Negative Integers m + 0 = 15Substitution m = 15Additive Identity Property I owe my mom twelve dollars. How much money do I need to earn to pay her back and still have three dollars for lunch?

Your Turn If each doughnut cost a half dollar, how many can I buy with my seven dollars? WorkJustification given equation Multiplicative Inverse Property and Multiplication Property of Equality 1d = 14Substitution Property d = 14Multiplicative Identity Property

Your Turn WorkJustification -52 = -4 fgiven equation -4f = -52Symmetric Property of Equality -4f/-4 = -52/-4Division Property of Equality 1f = 13 Substitution f = 13Multiplicative Identity Property I owe a total of $52. This is because I owe $4 to each friend I borrowed from. How many friends did I borrow money from?

Homework Holt Algebra 1 pages #30-48 even. Holt algebra 1 pages #26-44 evens. Justify each step!