Sophia Learning, College Algebra, Milestone 1

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18 questions were answered correctly. 2 questions were answered incorrectly. 1 Find the solution for x if |6x + 8|=32. • • • correct • RATIONALE To solve this equation, we will need to create two separate equations without absolute value bars. One equation will contain the expression exactly as it appears within the absolute value bars. The second equation must consider the case when the expression has the opposite value. Next, solve each equation separately, starting with 6x + 8=32. To solve for x, start by subtracting 8 from both sides. Your text here 1 CONCEPT Absolute Value Equations 2 Suppose that 3y – 5 = 45 and y = 3x – 2. Which of the following equations is equivalent to 3y – 5 = 45, but written only in terms of x? • 9x – 6 = 50 correct • 9x – 6 = 40 • 15x – 10 = 40 On the left, we have only 6x. On the right 32 minus 8 is 24. Then divide both sides by 6 to isolate x. The solution for the first equation is x = 4. The same process can be applied to the second equation 6x + 8 = -32. To solve, start by subtracting 8 from both sides. On the left, we have only 6x. On the right -32 minus 8 is -40. Then divide both sides by 6 to isolate x. The solution for the second equation is . The two solutions to |6x + 8| = 32 are x = 4 and . • 15x – 10 = 50 RATIONALE CONCEPT Substitution in multi-step linear equations 3 Jacob opened a money-market account. In the first month, he made an initial deposit of $500, and he plans to contribute an additional $75 every month. The account does not pay any interest. After how many months will he have a total of $1,475? • 12 months To find an equivalent equation written in terms of x we can use the second equation y = 3x – 2. This equation indicates that y is equivalent to 3x – 2 so we can substitute 3x – 2 in for y in the first equation 3y – 5 = 45. Now we have an equation in terms of x. To simplify it, first apply the Distributive Property and multiply 3 by the terms in the parentheses. 3 times 3x equals 9x, and 3 times -2 equals -6. Next, eliminate -5 from the left side of the equation by adding 5 to both sides. 45 plus 5 equals 50. This equation is equivalent to the original equation, but is written in terms of x. • 15 months • 13 months • 14 months correct RATIONALE Once each known value is substituted, we can solve for n. First, distribute 75 into (n – 1). 75(n – 1) is equivalent to 75n – 75. Next, combine like terms on the right side. 500 minus 75 is equal to 425. Subtract this value from both sides to isolate the n term. 1475 minus 425 equals 1050. Finally divide both sides by 75. 1050 divided by 75 is equal to 14. It will take 14 months for the balance to reach $1,475. The amount in Jacob's deposit account can be modeled using the formula for an arithmetic sequence. The term is the value after n months, is the initial balance, d is the common difference (or steady monthly deposits), and n is the number of months. Use the information provided to find each value. The initial deposit, , is $500. Jacob deposits $75 each month, which is the difference, d. We want to know how many months, n, it will take for the balance to reach $1475, whic

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