Question

Solve the inequality 14a/11>4/3, and write the solution in interval notation

Answer 1

To solve the inequality 14a/11 > 4/3, multiply both sides by 11, then by 3/44 to isolate a, yielding a > 1. The solution in interval notation is (1, ∞).

Step-by-step explanation:

The inequality we're solving is 14a/11 > 4/3. To solve this, we first multiply both sides of the inequality by 11 to get rid of the denominator on the left side:

1. 14a/11 * 11 > (4/3) * 11
2. 14a > 44/3
3. Next, we multiply both sides by 3/44 to isolate a on one side:
4. 14a * (3/44) > (44/3) * (3/44)
5. a > 1

So, the solution to the inequality is a > 1. In interval notation, the solution is expressed as >(1, ∞).

Answer 2

`a > (22)/(21)`

Step-by-step explanation:

Given the inequality function
`(14a)/(11)>(4)/(3)`, to write the inequality in interval notation, we need to first get the solution to the inequality as shown;

`(14a)/(11)>(4)/(3)\\cross\ multiply\\14a * 3 > 11 * 4\\42a >44\\divide \ both \ sides \ by \ 42\\(42a)/(42) > (44)/(42)\\ a>(22)/(21)`

Hence the expression in interval notation is
`a > (22)/(21)`