Chapter 8.5, Problem 28IP

(a)

To determine

The value of x

Answer to Problem 28IP

The solution of the equation is $x=5$ .

Explanation of Solution

Given:

The square

  

Concept Used:

• All sides of square are equal

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the value of x, in square all sides are equal so we equate the both sides as below:

  $4x=2x+10$

In order to find the solution of the equation $4x=2x+10$ first subtract both sides by $2x$ and then divide both sides by $2$ and then simplify further as below:

  $\begin{array}{l}4x=2x+10\\ 4x-2x=2x+10-2x\\ 2x=10\\ \frac{2x}{2}=\frac{10}{2}\\ x=5\end{array}$

Thus, the solution of the equation is $x=5$ .

(b)

To determine

The length of each sides of the square

Answer to Problem 28IP

The length of each side of square is $20$ .

Explanation of Solution

Given:

The solution of the equation is $x=5$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the sides of square we put the value of x in both sides as below:

  $\begin{array}{c}2x+10=2\cdot 5+10\\ =10+10\\ =20\\ 4x=4\cdot 5\\ =20\end{array}$

Thus, the length of each side of square is $20$ .