Question

Part a: solve –mk – 110 > 75 for m. Show your work. (4 points) part b: solve 2c – 8f = 24 for f. Show your work. (6 points)

Answer 1

(A)
-mk-110>75
-mk>185
mk<-185
m<-185/k

(B)
2c-8f=24
2c=24+8f
8f=2c-24
f=(2c-24)/8
f=1/4c-3

Answer 2

Part a:

Answer:

-mk - 110 < 75

-mk > 75 + 110

-mk > 185

mk < -185

m <
`(-185)/(k)`

Explanation:

Firstly, since you're only solving for m, k can be treated as a constant. The essence of the procedure to solve this is to position all the variable terms (terms with m) on one side of the inequality and all the constant terms (terms with only numbers and terms with k) on the other side. Then both sides can be simplified to determine m in terms of the constant terms.

With that in mind, starting with the given equation:

-mk - 110 > 75

Add 110 to both sides:

-mk - 110 + 110 > 75 + 110

Simplify:

-mk > 185

Divide both sides by k:

`(-mk)/(k)`>
`(185)/(k)`

Simplify:

-m >
`(185)/(k)`

Multiply both sides by -1. Note that when you multiply (or divide) an inequality by a negative number, you must flip the inequality:

-m × (-1) <
`(185)/(k)` × (-1)

Simplify:

m <
`(-185)/(k)`

Which gives you the final answer: m <
`(-185)/(k)`

Part b:

Answer:

2c - 8f = 24

-8f = 24 - 2c

-f =
`(24 - 2c)/(8)`

-f = 3 -
`(1)/(4)c`

f =
`(1)/(4)c - 3`

Explanation:

Firstly, since you're only solving for f, c can be treated as a constant. The essence of the procedure to solve this is to position all the variable terms (terms with f) on one side of the equality and all the constant terms (terms with only numbers and terms with c) on the other side. Then both sides can be simplified to determine f in terms of the constant terms.

Starting with the given equation:

2c - 8f = 24

Subtract 2c from both sides:

2c - 8f - 2c = 24 - 2c

Simplify:

-8f = 24 - 2c

Divide both sides by 8:

`(-8f)/(8)` =
`(24 - 2c)/(8)`

Simplify:

-f =
`(24)/(8)` -
`(2c)/(8)`

-f =
`3 - (1)/(4)c`

Multiply both sides by -1:

- f × (-1) = (
`3 -(1)/(4)c`) × (-1)

Simplify:

f =
`-3 + (1)/(4)c` =
`(1)/(4)c - 3`

Which gives us the final answer: f =
`(1)/(4)c - 3`