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Published byGladys Gaines Modified over 9 years ago

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1.3 Solving Equations Translating words in to math and Solving equations

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Words into math A few ways of saying Add; more, plus, increase by, sum To Subtract: less, minus, decreased by To Multiply: times, the product, twice, half To Divide: the quotient, would half also be a division statement? Square, Cube,…… the list goes on and on.

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A number means some variable 3 more than a number, would be 3 + x if I want x as the variable. Six times the cube of a number.6x 3 The square of a number decreased by the product of 5 and the numberx 2 - 5x Twice the difference of a number and 6 2(x – 6)

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How about the other way, math into words 14 + 9 = 23 Fourteen added to nine is twenty three 19 = 7y – 2 Nineteen is seven times a number minus 2

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Properties of Equality Addition property of equality. You can add the same number to both side of an equation. Multiply property of equality. You can multiply the same number, except zero, to both side of an equation.

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Here is how you would use the properties x – 8 = 12 add 8 to both side of the equation. x – 8 + 8 = 12 + 8 x + 0 = 20so x = 20 Multiply both side by 3, the fraction reduces.Thus x = 24

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Now for a problem with more then one step 53 = 3(y – 2) – 2(3y – 1) distribute 53 = 3y – 6 – 6y + 2 Add like terms 53 = - 3y -4 Add 4 and divide by – 3 57 = -3y - 19 = y or y = - 19

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We can use the properties to move equation around Distribute property Add like terms We use the addition property to move terms from side to side Multiplication property to solve the equation.

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To change a formula around Why would we do this to a formula? Given Solve for h To clear fractions, we can multiply by the common dominator, which in this case is 2

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We can go two ways at this point We can distribute or just divide I choose to divide by Giving Us

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Homework Page 24 – 26 # 19 – 23 odd, 29 – 39 odd, 41-46,47-51 odd, 57 – 60, 65, 67

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