Chapter 1.5, Problem 70PPSE

Solution

To solve the equation $3\left(x-2\right)+8=12$ .

  $x=\frac{10}{3}$

Given:

The equation, $3\left(x-2\right)+8=12$ .

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 $3\left(x-2\right)+8=12$ , isolate the variable on one side by performing the basic algebraic operations as shown below

  $\begin{array}{c}3\left(x-2\right)+8=12\\ 3\cdot x-3\cdot 2+8=12\\ 3x-6+8=12\\ 3x+2=12\\ 3x+2-2=12-2\\ 3x=10\\ \frac{3x}{3}=\frac{10}{3}\\ x=\frac{10}{3}\end{array}$

Thus, the required solution is $x=\frac{10}{3}$ .