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:

$\begin{gathered} \frac{16x}{16}=-\frac{2}{16} \\ =-\frac{1}{8} \\ \Rightarrow x=-\frac{1}{8} \end{gathered}$

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