Chapter A.9, Problem 18AYU

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 18AYU

a. $5 > 4$

b. $-3 > -4$

c. $6 > 3$

d. $-4 < -2$

Explanation of Solution

Given:

$2 > 1$

Calculation:

a. Adding 3 to each side of the given inequality. $2 + 3 > 1 + 3 \Rightarrow 5 > 4$

b. Subtracting 5 from each side of the given inequality. $2-5 > 1 - 5 \Rightarrow -3 > -4$

c. Multiplying each side of the given inequality by 3. $2 \cdot 3 > 1 \cdot 3 \Rightarrow 6 > 3$

d. Multiplying each side of the given inequality by $-2$. $2 \cdot \left(-2\right) > 1 \cdot \left(-2\right) \Rightarrow -4 < -2$