Question

15-4(n+7)<2a+17
Solve for a

Answer 1

Answer: a>-2n+13

Explanation:

15-4n+28<2a+17 : Given

43-4n<2a+17 : Combine Like terms

26-4n<2a : Subtraction property of equality (subtract 17 on both sides)

13-2n<a : Division property of equality (divide both sides by 2)

a>-2n+13 : Reflexive property (swap)

Answer 2

a > -2n - 14

Explanation:

In order to solve the inequality 15 - 4(n + 7) < 2a + 17 for a, we can follow these steps:

Distribute the -4 in the left-hand side:

15 - 4(n + 7) < 2a + 17

15 - 4n - 28 < 2a + 17

Combine the constant terms on the right-hand side:

-4n - 13 < 2a + 17

Subtract 17 in both sides:

-4n - 13 - 17 < 2a + 17 - 17

2a > - 4n - 30

Divide both sides by 2:

`\sf (2a )/(2) > (- 4n - 30)/(2)`

a > - 2n - 14

Since a can be any number greater than -15 - 2n, the solution to the inequality is:

a > -2n - 14

Note: This is the most general solution to the inequality. If we have any specific values for n, we can substitute them into the inequality to get a more specific solution.