Chapter 8, Problem 19CR

To determine

The solution of the equation $3\left(x-5\right)=24$ ,

Answer to Problem 19CR

  $x=13$

Explanation of Solution

Given:

The equation, $3\left(x-5\right)=24$

Concept Used:

Left distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

• 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 $3\left(x-5\right)=24$ for the variable, isolate the variable term x on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate x on left side, first use Left distributive property and then add both sides by $15$ and then divide both sides by $3$ and then simplify further as shown below,

  $\begin{array}{c}3\left(x-5\right)=24\\ 3\cdot x-3\cdot 5=24\\ 3x-15=24\\ 3x-15+15=24+15\\ 3x=39\\ \frac{3x}{3}=\frac{39}{3}\\ x=13\end{array}$

Thus, the solution of the given equation is $x=13$ .