Question

Match each equation with its solution.

1. n/8 + 1/2 = -3 1/2. A. n = -3.2
2. -1.4n + 2.1 = 6.58. B. n = -0.2
3. 5.7n + 4.1 = 2.96. C. n = -32
4. 4n - 2 3/4 = -22 3/4. D. n = -5

Answer 1

To match each equation with its solution, solve each equation and find the corresponding value of n. For these equations, the matches are (1) C (n = -32), (2) A (n = -3.2), (3) B (n = -0.2), and (4) D (n = -5).

Step-by-step explanation:

The question involves solving four different equations and matching each to its corresponding solution. Let's solve them step by step.

1. For the equation n/8 + 1/2 = -3 1/2, convert -3 1/2 to an improper fraction: -7/2. Multiply both sides by 8 to eliminate the fraction for n, resulting in n + 4 = -28, and solve for n to get n = -32. So, 1 matches with C.
2. In the -1.4n + 2.1 = 6.58 equation, first subtract 2.1 from both sides to get -1.4n = 4.48. Divide by -1.4 to find n = -3.2. So, 2 matches with A.
3. For 5.7n + 4.1 = 2.96, subtract 4.1 from both sides to obtain 5.7n = -1.14. Divide by 5.7 to find n = -0.2. So, 3 matches with B.
4. In the last equation, 4n - 2 3/4 = -22 3/4, first convert -2 3/4 to an improper fraction: -11/4. Do the same for -22 3/4 to get -91/4 and then add 11/4 to both sides to get 4n = -80/4, or 4n = -20. Divide both sides by 4 to find n = -5. Thus, 4 matches with D.

Using the solutions obtained, we can match each equation with its correct solution. The completed matches are: (1) C (n = -32), (2) A (n = -3.2), (3) B (n = -0.2), and (4) D (n = -5).