Chapter A.9, Problem 22AYU

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 22AYU

a. $0 > 2$

b. $-8 > -10$

c. $-9 > -15$

d. $6 < 10$

Explanation of Solution

Given

$1 - 2x > 5$

Calculation:

a. Adding 3 to each side of the given inequality. $1 - 2x + 3 > 5 + 3 \Rightarrow 4-2x > 8$

b. Subtracting 5 from each side of the given inequality. $1 - 2x - 5 > 5 - 5 \Rightarrow -4 - 2x > 0$

c. Multiplying each side of the given inequality by 3. $\left(1 - 2x\right) \cdot 3 > 5 \cdot 3 \Rightarrow 3 - 6x > 15$

d. Multiplying each side of the given inequality by $-2$. $\left(1 - 2x\right) \cdot \left(-2\right) > \left(5\right) \cdot \left(-2\right) \Rightarrow -2 + 4x < -10$