Chapter 8.4, Problem 20IP

To determine

The solution of the equation $\frac{4}{5}(2+m)=24$ .

Answer to Problem 20IP

  $m=28$

Explanation of Solution

Given:

The equation, $\frac{4}{5}(2+m)=24$ .

Concept Used:

Distributive property:

Left Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$

Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$

• 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 $\frac{4}{5}(2+m)=24$ for the unknown variable, first using left Distributive property on left side of the equation and then isolate the variable term m on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate m on left side, first subtract 8/5 from both sides and then multiplying both sides by 5/4 and then simplify further as shown below,

  $\begin{array}{l}\frac{4}{5}(2+m)=24\\ \frac{4}{5}\cdot 2+\frac{4}{5}\cdot m=24\\ \frac{8}{5}+\frac{4}{5}m=24\\ \frac{8}{5}-\frac{8}{5}+\frac{4}{5}m=24-\frac{8}{5}\\ \frac{4}{5}m=\frac{112}{5}\\ \frac{4}{5}m\times \frac{5}{4}=\frac{112}{5}\times \frac{5}{4}\\ m=28\end{array}$

Thus, the solution of the given equation is $m=28$ .