Switch sides.
Break down the problem into these 2 equations.
Solve the 1st equation: \(6=-2x-|4+x|\).
Break down the problem into these 2 equations.
\[6=-2x-(4+x)\]
\[6=-2x--(4+x)\]
Solve the 1st equation: \(6=-2x-(4+x)\).
Remove parentheses.
\[6=-2x-4-x\]
Simplify \(-2x-4-x\) to \(-3x-4\).
\[6=-3x-4\]
Add \(4\) to both sides.
\[6+4=-3x\]
Simplify \(6+4\) to \(10\).
\[10=-3x\]
Divide both sides by \(-3\).
\[-\frac{10}{3}=x\]
Switch sides.
\[x=-\frac{10}{3}\]
\[x=-\frac{10}{3}\]
Solve the 2nd equation: \(6=-2x--(4+x)\).
Remove parentheses.
\[6=-2x--4-x\]
Simplify \(-2x--4-x\) to \(-2x+4-x\).
\[6=-2x+4-x\]
Simplify \(-2x+4-x\) to \(-3x+4\).
\[6=-3x+4\]
Subtract \(4\) from both sides.
\[6-4=-3x\]
Simplify \(6-4\) to \(2\).
\[2=-3x\]
Divide both sides by \(-3\).
\[-\frac{2}{3}=x\]
Switch sides.
\[x=-\frac{2}{3}\]
\[x=-\frac{2}{3}\]
Collect all solutions.
\[x=-\frac{10}{3},-\frac{2}{3}\]
Check solution
When \(x=-\frac{2}{3}\), the original equation \(6=-2x-|4+x|\) does not hold true.We will drop \(x=-\frac{2}{3}\) from the solution set.
Therefore,
Solve the 2nd equation: \(6=x\).
Collect all solutions.
