You earned the following scores on five science tests: 75, 82, 90,84, and 71. You want to have an average score of at least 80 after you take the sixth test.

a. Write and solve an inequality to find the possible schores that you can earn on your sixth test in order to meet your goal.

( 75 + 82 + 90 + 84 + 71 + n ) / 6 > OR = 80 Multiplly both sides by 6

75 + 82 + 90 + 84 + 71 + n > OR = 6 * 80

402 + n > OR = 480

n > OR = 480 - 402

n > OR = 78

To find the possible scores you can earn on the sixth test to meet your goal of having an average score of at least 80, we can use the following steps:

Step 1: Find the sum of your current scores: 75 + 82 + 90 + 84 + 71 = 402.
Step 2: Determine the number of tests taken, which is 5.

Let's assume the score you earn on the sixth test is denoted by x.

Step 3: Write the inequality based on the given conditions:
(402 + x) / 6 ≥ 80

Here:
- (402 + x) represents the sum of your current scores (402) plus the unknown score on the sixth test (x).
- Dividing the sum by 6 gives the average score.
- Setting this average to be greater than or equal to 80 represents the goal of having an average score of at least 80.

Step 4: Solve the inequality:
(402 + x) / 6 ≥ 80

To isolate x, multiply both sides of the inequality by 6:
402 + x ≥ 480

Step 5: Solve for x:
x ≥ 480 - 402
x ≥ 78

Thus, the possible scores that you can earn on your sixth test in order to meet your goal of having an average score of at least 80 are 78 or any score greater than 78.