Chapter 1.4, Problem 24PPSE

Solution

The solution of the equation $5\left(2-g\right)=0$ , and check the answer.

  $g=2$

Given:

The equation, $5\left(2-g\right)=0$ .

Concept Used:

• The opposite operation of addition is subtraction and the opposite operation of subtraction is addition.
• The opposite operation of multiplication is division and the opposite operation of division is multiplication.
• Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

Calculation:

In order to solve the given equation $5\left(2-g\right)=0$ , isolate the variable on left side by performing the basic algebraic operations as shown below

  $\begin{array}{c}5\left(2-g\right)=0\\ 5\cdot 2-5\cdot g=0\\ 10-5g=0\\ 10-10-5g=0-10\\ -5g=-10\\ \frac{-5g}{-5}=\frac{-10}{-5}\\ g=2\end{array}$

Thus, the solution of the equation is $g=2$ .

To check the answer, substitute $g=2$ into the given equation and show that the left-hand side expression is equal to the right-hand side expression as shown below

  $\begin{array}{c}5\left(2-g\right)=0\\ 5\left(2-2\right)=0\\ 5\left(0\right)=0\\ 0=0\text{True statement}\end{array}$