Question

Part A: Solve −np − 80 < 60 for n. Show your work. (4 points)

Part B: Solve 2a − 5d = 30 for d. Show your work. (6 points)

Answer 1

Part A ⇒ n>-140/p and p≠0

Part B. ⇒ d=-30-2a/5

Explanation:

Part A. -np-80<60

First, add by 80 both sides of equation.

-np-80+80<60+80

Simplify.

60+80=140

-np<140

Then, multiply by -1 both sides of equation.

(-np)(-1)>140(-1)

Simplify.

np>-140

Divide by p both sides of equation.

np/p>-140/p; p≠0

Simplify to find the answer.

n>-140/p; p≠0 is the correct answer from part a.

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Part B. 2a-5d=30

First add by 2a from both sides of equation.

2a-5d+2a=30+2a

Then, simplify.

-5d=30-2a

Divide by -5 from both sides of equation.

-5d/-5=30/-5-2a/5

Simplify, to find the answer.

d=-30-2a/5 is the correct answer from part b.

Answer 2

Part A:

For this case we have the following inequality:

`-np-80 <60`

We add 80 to both sides of the inequality:

`-np <60+80\\-np <140`

Dividing between -p on both sides, having to change the inequality sign:

`n> - \frac {140} {p}`

Part B:

For this case we have the following equation:

`2a-5d = 30`

Subtracting 2a on both sides:

`-5d = 30-2a`

Dividing between -5 on both sides:

`d = \frac {30-2a} {- 5}\\d = \frac {-30+2a} {5}\\d = - \frac {30} {5} +\frac {2a} {5}\\d = -6+ \frac {2a} {5}`

Answer:

`n> - \frac {140} {p}\\d = -6+\frac {2a} {5}`