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Equations and Inequalities CHAPTER 4

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Look at this picture. The paper bag on the left contains a certain number of orange blocks. Assuming that the paper bag weighs nothing, can you determines how many blocks are in the orange bag? What do you think we could do? One way is to remove four orange blocks from each side of the balance. The bag contains three blocks. In algebra, an EQUATION is like a balance. The weights on each side of the scale are equal. You can use algebra tiles to model and solve equations. 4-1-C: EXPLORE – SOLVE EQUATIONS USING ALGEBRA TILES

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1 x

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4-1-D: SOLVE ONE-STEP ADDITION AND SUBTRACTION EQUATIONS

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a = 7 r = 7 x = -3 y = -4 If you are ever stuck and do not know what to do, ask yourself these three questions: 1.What is my variable? 2.What is being done to my variable? 3.How can I UNDO what is being done to my variable?

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4-1-D: SOLVE ONE-STEP ADDITION AND SUBTRACTION EQUATIONS

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s = 17 w = 18 x = 7 y = 11 On your own, practice solving addition and subtraction equations by completing #1 - 8 on page 211 in your math book.

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4-2-B: SOLVE ONE STEP MULTIPLICATION AND DIVISION EQUATIONS

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c

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e = 3 j = -9 x = -5 y = 4

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4-2-B: SOLVE ONE STEP MULTIPLICATION AND DIVISION EQUATIONS

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m = 70 h = -36 x =150 y = 80 On your own, practice solving multiplication and division equations by completing #1 - 8 on page 218 in your math book.

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4-2-D: SOLVE EQUATIONS WITH RATIONAL COEFFICIENTS

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On your own, practice solving equations with rational coefficients by completing # on page 224 in your math book.

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4-3-B: SOLVE TWO STEP EQUATIONS In order of operations, the multiplication would be evaluated first. But because we are doing things in the reverse order, we must UNDO the addition first. After the first step, were left with a one-step division equation!

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4-3-B: SOLVE TWO STEP EQUATIONS STEP 1 STEP 2

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4-3-B: SOLVE TWO STEP EQUATIONS x = 3 y = - 3 m = - 4 r = 2.4 s = - 4 q = 48 d = 8 p = - 9 On your own, practice solving two-step equations by completing #1 - 7 on page 232 in your math book.

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As you discovered in the Geology Rocks Equations activity, you can use the properties of equality with variables on each side. The new equation is equivalent to the original equation. Remember the four properties of equality: 1.Subtraction Property of Equality 2.Addition Property of Equality 3.Division Property of Equality 4.Multiplication Property of Equality Key Concepts: We have to use the equality properties in order to get the variable on to ONE side of the equation. We can only solve the equation if we can ISOLATE the variable. Remember that what you do to one side of the equation, you MUST do the EXACT SAME THING to the other side of the equation. 4-3-D: SOLVE EQUATIONS WITH VARIABLES ON BOTH SIDES

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x = 6 x = 24 x = 4.2 x = - 10 x = ¼ x = -6

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4-3-D: SOLVE EQUATIONS WITH VARIABLES ON BOTH SIDES

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4-4-B: SOLVE INEQUALITIES BY ADDITION OR SUBTRACTION

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Inequalities Words is less than is fewer than is greater than is more than exceeds is less than or equal to is no more than is at most is greater than or equal to is no less than is at least Symbols Check out a few examples! 4-4-B: SOLVE INEQUALITIES BY ADDITION OR SUBTRACTION

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4-4-C: SOLVE INEQUALITIES BY MULTIPLICATION AND DIVISION

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FLIPPED

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SOLVING 2-STEP INEQUALITIES v > 5 r > 9 x 8 m -6 n > 5 x 15 x > -9 m < -4

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