Section 2.4 More on Solving Linear Equations 127 y - 5 4 1d. - 2y 9 = 1 6 36a y - 5 4 - 2y 9 b = 36a1 6 b Multiply each side by the LCD, 36. 36a y - 5 4 b - 36a 2y 9 b = 6 Apply the distributive property. Simplify. 9(y - 5) - 4(2y) = 6 Simplify each product. 9y - 45 - 8y =6 Multiply the remaining factors. y - 45 =6 Simplify each side. y - 45 + 45 = 6 + 45 Add 45 to each side. y = 51 Simplify. y - 5 4 Check: - 2y 9 = 1 6 Original equation 51 - 5 4 - 2(51) 9 = 1 6 Replace y with 51. 46 4 - 102 9 = 1 6 Simplify the numerators. 414 36 - 408 36 = 6 36 Write equivalent fractions with LCD, 36. 6 36 = 6 36 Simplify. Since y = 51 makes the equation true, the solution set is {51}. Student Check 1 Solve each equation by first clearing fractions. Check each answer. a. 7x 6 - 4 = x 6 b. y 4 - 1 12 = y 8 c. 3 4 (x - 8) = 2 7 (x + 14) d. a + 7 3 - 4 = a 6 ������������ When we multiply an equation by the LCD of all the fractions in the equation, the resulting equation should not have any fractions. If the resulting equation still contains fractions, then we either simplified incorrectly or calculated the LCD incorrectly. Linear Equations Containing Decimals As with equations that contain fractions, equations containing decimals can also be tedious to solve by hand. So, we will clear the decimals from the equation. Consider the following products. Recall that multiplying a number by a power of 10 moves the decimal point to the right. ()* 10(3.2 y ) = ( 1 0 ) ( 3 . 2 ) y = 32y One decimal place Multiplying an expression with one decimal place by 101 or 10 clears the decimal from the expression. Objective 2 ▶ Solve linear equations with decimals.
hendricks_beginning_algebra_1e_ch1_3
To see the actual publication please follow the link above