Question

Solve the equation 3(x+1)=5-2(3x+4)

Answer 1

`3(x+1)=5-2(3x+4)`

To solve the given equation:

1. Remove parenthesis:

Use distributive property:

`a(b+c)=ab+ac`
`3x+3=5-6x-8`

2. Combine like terms:

`3x+3=-6x-3`

3. Substract 3 in both sides of the equation:

`\begin{gathered} 3x-3+3=-6x-3+3 \\ \\ 3x=-6x \end{gathered}`

4. Add 6x in both sides of the equation:

`\begin{gathered} 3x+6x=-6x+6x \\ 9x=0 \end{gathered}`

5. Divide into 9 both sides of the equation: (0 divided into any number is equal to 0)

`\begin{gathered} (9)/(9)x=(0)/(9) \\ \\ x=0 \end{gathered}`

6. Prove the x=0 in the original equation:

`\begin{gathered} 3(0-1)=5-2(3(0)+4) \\ 3(-1)=5-2(4) \\ -3=5-8 \\ -3=-3 \end{gathered}`

As x=0 make a true the equation (-3 is equal to -3). The solution is correct

The solution for the equation is x=0