Respuesta :
Answer:
In the two different ways we have solved the given equation as [tex]x=\frac{1}{2}[/tex]
Step-by-step explanation:
Given expression is [tex]\frac{2}{3}(3x+6)=4x+3[/tex]
To simplify the given expression in two ways:
First way:
Given [tex]\frac{2}{3}(3x+6)=4x+3[/tex]
[tex]\frac{2}{3}(3x+6)=4x+3[/tex]
[tex]\frac{6x+12}{3}=4x+3[/tex]
Multiplying 3 on both sides
[tex]3\times (\frac{6x+12}{3})=3\times (4x+3)[/tex]
[tex]6x+12=12x+9[/tex]
[tex]6x+12-12x-9=0[/tex] (adding the like terms)
[tex]-6x+3=0[/tex]
[tex]3(-2x+1)=0[/tex]
Dividing by 3 on both sides
[tex]3(-2x+1)\times \frac{1}3}=0\times \frac{1}3}[/tex]
[tex](-2x+1)=0[/tex]
[tex]-(2x-1)=0[/tex]
[tex]2x-1=0[/tex]
[tex]x=\frac{1}{2}[/tex]
Therefore the given expression is solved that [tex]x=\frac{1}{2}[/tex]
Another way:
Given [tex]\frac{2}{3}(3x+6)=4x+3[/tex]
[tex]\frac{2}{3}(3x+6)=4x+3[/tex]
[tex]2(\frac{3x}{3}+\frac{6}{3})=4x+3[/tex]
[tex]2(x+2)=4x+3[/tex]
[tex]2x+4=4x+3[/tex]
[tex]4x+3-2x-4=0[/tex] (adding the like terms)
[tex]2x-1=0[/tex]
[tex]x=\frac{1}{2}[/tex]
Therefore the given expression is solved that [tex]x=\frac{1}{2}[/tex]
In the two different ways we have solved the given equation as [tex]x=\frac{1}{2}[/tex]
