Question

Solve : 4(3x+1)=2(1-2x)

Answer 1

Starting with the equation:

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

Use the distributive property to expand both parenthesis:

`4\cdot3x+4\cdot1=2\cdot1-2\cdot2x`

Simplify the products:

`12x+4=2-4x`

Add 4x to both sides of the equation and then add like terms:

`\begin{gathered} 12x+4+4x=2-4x+4x \\ \Rightarrow16x+4=2 \end{gathered}`

Substract 4 from both sides of the equation, then simplify:

`\begin{gathered} 16x+4-4=2-4 \\ \Rightarrow16x=-2 \end{gathered}`

Divide both sides of the equation by 16 to isolate x:

`\begin{gathered} (16x)/(16)=-(2)/(16) \\ =-(1)/(8) \\ \Rightarrow x=-(1)/(8) \end{gathered}`

Check this answer by plugging in x=-1/8 into the original equation and verifying that the same number is obtained in both sides.