Hello there!
Given the equation below:
[tex] \displaystyle \large{ \frac{3x + 3}{2} = 9}[/tex]
Our first step is to get rid of the denominator by multiplying the whole equation by 2.
[tex] \displaystyle \large{ \frac{3x + 3}{2} \cdot 2 = 9 \cdot 2} \\ \displaystyle \large{ 3x + 3 = 18}[/tex]
Isolate x-term - first, we subtract 3 both sides.
[tex] \displaystyle \large{3x + 3 - 3 = 18 - 3} \\ \displaystyle \large{3x= 15} \\ [/tex]
Divide both sides by 3 to leave only x-term.
[tex] \displaystyle \large{ \frac{3x}{3} = \frac{15}{3} } \\ \: \displaystyle \large{x = 5}[/tex]
Therefore, the value of x is 5.
Checking Answer
Optional Step:
First, we substitute x-value that we got in the equation.
[tex] \displaystyle \large{ \frac{3x + 3}{2} = 9} \\ \displaystyle \large{ \frac{3(5)+ 3}{2} = 9}[/tex]
Evaluate the expression.
[tex] \displaystyle \large{ \frac{15 + 3}{2} = 9} \\ \displaystyle \large{ \frac{18}{2} = 9} \\ \displaystyle \large{ 9 = 9}[/tex]
Since both sides are equal. The equation is true!
Answer
Hence, x = 5.
Let me know if you have any questions!
Topic: Linear Equation
