Chapter A.9, Problem 21AYU

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 21AYU

a. $2x + 4 < 5$

b. $2x-4 < -3$

c. $6x + 3 < 6$

d. $-4x-2 > -4$

Explanation of Solution

Given

$2x + 1 < 2$

Calculation:

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

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

c. Multiplying each side of the given inequality by 3. $\left(2x + 1\right) \cdot 3 < 2 \cdot 3 \Rightarrow 6x + 3 < 6$

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