Chapter 15.1, Problem 1PSA

(a)

To determine

To Find: The solution of variable by solving the inequality.

Answer to Problem 1PSA

  $x>25$

Explanation of Solution

Given:

  $\frac{3}{5}x>15$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

  $\begin{array}{l}\frac{3}{5}x>15\\ \text{⇒}3x>15\times 5\\ \text{⇒}x>\frac{75}{3}\\ \text{⇒}x>25\end{array}$

Conclusion:

Thus the required solution is $x>25$ .

(b)

To determine

To Find: The solution of the variable by solving inequality.

Answer to Problem 1PSA

  $x=6$

Explanation of Solution

Given:

  $5x-4>26$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

  $\begin{array}{l}5x-4>26\\ \text{⇒}5x>26+4\\ \text{⇒}5x=30\\ \text{⇒}x=\frac{30}{5}\\ \text{⇒}x=6\end{array}$

Conclusion:

Thus the required solution is $x=6$ .

(c)

To determine

To Find: The solution of the variable by solving inequality.

Answer to Problem 1PSA

  $x\ge -7$

Explanation of Solution

Given:

  $-4x\le 28$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

  $\begin{array}{l}-4x\le 28\\ \text{⇒}-x\le \frac{28}{4}\\ \text{⇒}-x\le 7\\ \text{⇒}x\ge -7\end{array}$

Conclusion:

Thus the required solution is $x\ge -7$

(d)

To determine

To Find: The solution of the variable by solving inequality.

Answer to Problem 1PSA

  $1<x$

Explanation of Solution

Given:

  $10-x<8x-\left(2x-3\right)$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

  $\begin{array}{l}10-x<8x-\left(2x-3\right)\\ \text{⇒}10-x<8x-2x+3\\ \text{⇒}10-3<6x+x\\ \text{⇒}7<7x\\ \text{⇒}1<x\end{array}$

Conclusion:

Thus the required solution is $1<x$ .