Chapter A.9, Problem 17AYU

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 17AYU

a. $6 < 8$

b. $-2 < 0$

c. $9 < 15$

d. $-6 > -10$

Explanation of Solution

Given:

$$ 3 < 5$$

Calculation:

a. Adding 3 to each side of the given inequality. $3 + 3 < 5 + 3 \Rightarrow 6 < 8$

b. Subtracting 5 from each side of the given inequality. $3 - 5 < 5 - 5 \Rightarrow -2 < 0$

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 $-2$. $3 \cdot \left(-2\right) < 5 \cdot \left(-2\right) \Rightarrow -6 > -10$