To solve the inequality [tex]\(-72 > -56i\)[/tex], follow these steps:
1. Isolate [tex]\(i\)[/tex]:
- Divide both sides of the inequality by [tex]\(-56\)[/tex]. Remember, dividing an inequality by a negative number reverses the direction of the inequality.
[tex]\[
\frac{-72}{-56} < i
\][/tex]
2. Simplify the fraction:
- Simplifying [tex]\(\frac{-72}{-56}\)[/tex], both the numerator and the denominator are negative, so the fraction will be positive.
[tex]\[
\frac{72}{56} < i
\][/tex]
3. Reduce the fraction to its simplest form:
- Divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 72 and 56 is 8.
[tex]\[
\frac{72 \div 8}{56 \div 8} < i \quad \Rightarrow \quad \frac{9}{7} < i
\][/tex]
4. Convert the fraction to decimal:
- To express the fraction [tex]\(\frac{9}{7}\)[/tex] as a decimal, divide 9 by 7.
[tex]\[
\frac{9}{7} \approx 1.2857
\][/tex]
- Round this decimal to two decimal places for simplicity.
[tex]\[
\frac{9}{7} \approx 1.29
\][/tex]
Therefore, the simplified solution to the inequality [tex]\(-72 > -56i\)[/tex] is:
[tex]\[
i > 1.29
\][/tex]
So, the solution is:
[tex]\[
\boxed{i > 1.29}
\][/tex]
