Question

A. (100 + 82 + 70 + 72 + 80 + x)/6 ≤ 80
(404 + x)/6 ≤ 80
(404 + x)/6 X 6 ≤ 80 X 6
404 + x ≤ 480
404 + x - 404 ≤ 480 - 404
x = 76

B.
The minimum grade that Sam must earn in order to keep a B average in math is 76%.

Is this correct?
Or does it need to be an equals sign? I need it to be an algebraic inequality though.

Answer 1

x≤76

Sam needs at least a 76, so he could have more.

Answer 2

Why is it less than or equal to? Doesn't he need more? Since he needs a B average?

Answer 3

You're right. It does need to be greater than or equal to. Your work, however, shows that hs average needs to be less than or equal to 80. I apologize.

Answer 4

ohhhh can you tell me how to fix it?

Answer 5

\[80 \le \frac{100+82+70+80+x}{6} \le 89.99999999\]

Answer 6

Flip the sign in your first line of work, and in all subsequent lines.

Answer 7

\[80 \le \frac{100+82+70+80+x}{6} < 90\]
this is one is better than mine other inequality

Answer 8

so, 80 should be like this:\[80\ge\] instead?

Answer 9

Like this:
80 ≤ (100 + 82 + 70 + 72 + 80 + x)/6

Answer 10

ohhhh I see

Answer 11

should it be like this? x \[\le\] 76?

Answer 12

oh i missed one number 72in my inequalities above
\[480 \le 404+x <540\]
\[76 \le x <136\]

to make a B x needs to be between =76 and 136 (but part of this range is impossible)
so really to make a B you need between =76 and =100
the minimum you need to make is a 76 to make a B

Answer 13

Ohhh I see, so is this right?
80 ≤ (100 + 82 + 70 + 72 + 80 + x)/6 < 90
80 ≤ (404 + x)/6 < 90
80 X 6 ≤(404 + x)/6 X 6 < 90 X 6
480 ≤ 404 + x < 540
480 - 404 ≤404 + x - 404 < 540 - 404
76 ≤ x < 136
x = 76

Answer 14

x ≤ 76 at the end right?

Answer 15

no x greater than or equal to 76 not less than of equal to

Answer 16

ohhh ok

Answer 17

Thank you for your help!