Chapter A.9, Problem 20AYU

To determine

To write: The inequality obtained by:

a. Adding 3 to each side of the given inequality.

b. Subtracting 5 from each side of the given inequality.

c. Multiplying each side of the given inequality by 3.

d. Multiplying each side of the given inequality by $-2$.

Answer to Problem 20AYU

a. $0 > -2$

b. $-8 > -10$

c. $-9 > -15$

d. $6 < 10$

Explanation of Solution

Given:

$-3 > -5$

Calculation:

a. Adding 3 to each side of the given inequality. $-3 + 3 > -5 + 3 \Rightarrow 0 > -2$

b. Subtracting 5 from each side of the given inequality. $-3 - 5 > -5 - 5 \Rightarrow -8 > -10$

c. Multiplying each side of the given inequality by 3. $-3 \cdot 3 > -5 \cdot 3 \Rightarrow -9 > -15$

d. Multiplying each side of the given inequality by $-2$. $\left(-3\right) \cdot \left(-2\right) > \left(-5\right) \cdot \left(-2\right) \Rightarrow 6 < 10$