Question 212470
Solve:
{{{abs(-x+4) = abs(4x+2)}}} Remove the absolute-value bars and write the two equations:
{{{-x+4 = 4x+2}}} or {{{-x+4 = -(4x+2)}}}
Starting with the first equation:
{{{-x+4 = 4x+2}}} Add x to both sides of the equation to get the x's on one side of the equation.
{{{cross(-x+x)+4 = x+4x+2}}} The x's on the left sides disappear and the x's on the right side get added together.
{{{4 = 5x+2}}} Now subtract 2 from both sides.
{{{4-2 = 5x+2-2}}}}
{{{2 = 5x}}} Finally, divide both sides by 5.
{{{2/5 = x}}} or {{{highlight(x = 2/5)}}}

For the second equation we have:
{{{-x+4 = -(4x+2)}}} Apply the "distributive property" to the right side of the equation.
{{{-x+4 = -4x-2}}} Now add 4x to both sides to get the x's on one side of the equation.
{{{highlight_green(4x-x+4) = cross(-4x+4x)-2}}} The x's on the right side disappear and the x's on the left side are subtracted.
{{{3x+4 = -2}}} Subtract 4 from both sides.
{{{3x+cross(4-4) = -2-4}}} The 4's on the left side disappear.
{{{3x = -6}}} Finally, divide both sides by 3.
{{{highlight(x = -2)}}}