Chapter 8.4, Problem 34IP

To determine

The solution of the equation $4(x-5)+3=31$ .

Answer to Problem 34IP

  $x=12$

Explanation of Solution

Given:

The equation, $4(x-5)+3=31$ .

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 solve the given equation $4(x-5)+3=31$ for the unknown variable, first multiplying 4 inside the bracket then adding the numbers which are without variable, now the equation is as shown below:

  $\begin{array}{l}4(x-5)+3=31\\ 4x-20+3=31\\ 4x-17=31\end{array}$

Here to isolate x on left side, first add 17 both sides and then divide both sides by 4 and then simplify further as shown below,

  $\begin{array}{l}4x-17=31\\ 4x-17+17=31+17\\ 4x=48\\ \frac{4x}{4}=\frac{48}{4}\\ x=12\end{array}$

Thus, the solution of the given equation is $x=12$ .