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Solving Multi-Step Equations by Clearing the Fractions

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Solving Two-Step Equations That Contain Fractions – Ex. 1 Solve Multiply every term on both sides by 4, the LCD of the fractions. Distribute 4 on the left and right side. Method: Multiply every term on both sides by the LCD to clear the fractions. 2x + 8 = 3 - 8 -8 Simplify. Since 8 is added to 2x, subtract 8 on both sides to undo the addition. 2x = -5

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Solve 2 Since x is multiplied by 2, divide both sides by 2 to undo the multiplication. 2x = -5 Solving Two-Step Equations That Contain Fractions – Ex. 1 (cont.) Method: Multiply every term on both sides by the LCD to clear the fractions.

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Solve Method: Multiply by the LCD to clear the fractions. Multiply every term on both sides by 14, the LCD of the fractions. +2 4x = 5 4 x = 5/4 Solving Two-Step Equations That Contain Fractions – Ex. 2

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Solving Two-Step Equations That Contain Fractions – Ex. 3 Solve Method: Multiply by the LCD to clear the fractions. Multiply both sides by 12, the LCD of the fractions. 8r + 9 = 7 –9 8r = –2 Distribute 12 to every term on both sides. Simplify. Since 9 is added to 8r, subtract 9 from both sides to undo the addition.

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Solving Two-Step Equations That Contain Fractions – Ex. 3 (cont.) Solve 8r = –2 8 Since r is multiplied by 8, divide both sides by 8 to undo the multiplication.

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Solving Two-Step Equations That Contain Fractions – Ex. 4 Solve Multiply both sides by 24, the LCD of the fractions. Distribute 24 on both sides. Method: Multiply by the LCD to clear the fractions. 3y – 18 = 14 +18 Simplify. Since 18 is subtracted from 3y, add 18 to both sides to undo the subtraction. 3y = 32

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Solve 3 Since y is multiplied by 3, divide both sides by 3 to undo the multiplication. 3y = 32 Solving Two-Step Equations That Contain Fractions – Ex. 4 (cont.)

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Solving Two-Step Equations That Contain Decimals – Ex. 5 Solve 0.6x + 2.1 = 4.5 Multiply every terms on both sides by 10 because all decimals are to the tenths place. (If decimals were to hundredths place, you would multiply by 100.) Method: Multiply both sides by the same power of 10 to clear the decimals. 10(0.6x) + 10(2.1) = 10(4.5) 6x+ 21 = 45 –21 -21 6x = 24 6 x = 4

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Workbook pg. 304, #3 pg. 305, #5, 6 pg. 315, #17

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