Question

Show two different ways to solve 2/3(3x+6)=4x+3

Answer 1

Answer:

In the two different ways we have solved the given equation as $x=\frac{1}{2}$

Step-by-step explanation:

Given expression is $\frac{2}{3}(3x+6)=4x+3$

To simplify the given expression in two ways:

First way:

Given  $\frac{2}{3}(3x+6)=4x+3$

$\frac{2}{3}(3x+6)=4x+3$

$\frac{6x+12}{3}=4x+3$

Multiplying 3 on both sides

$3\times (\frac{6x+12}{3})=3\times (4x+3)$

$6x+12=12x+9$

$6x+12-12x-9=0$  (adding the like terms)

$-6x+3=0$

$3(-2x+1)=0$

Dividing by 3 on both sides

$3(-2x+1)\times \frac{1}3}=0\times \frac{1}3}$

$(-2x+1)=0$

$-(2x-1)=0$

$2x-1=0$

$x=\frac{1}{2}$

Therefore the given expression is solved that $x=\frac{1}{2}$

Another way:

Given  $\frac{2}{3}(3x+6)=4x+3$

$\frac{2}{3}(3x+6)=4x+3$

$2(\frac{3x}{3}+\frac{6}{3})=4x+3$

$2(x+2)=4x+3$

$2x+4=4x+3$

$4x+3-2x-4=0$ (adding the like terms)

$2x-1=0$

$x=\frac{1}{2}$

Therefore the given expression is solved that $x=\frac{1}{2}$

In the two different ways we have solved the given equation as $x=\frac{1}{2}$