Factor out the common term \(2\).
\[6-\frac{2(1+x)}{5}\ge \frac{2-3x}{4}\]
Multiply both sides by \(20\) (the LCM of \(5, 4\)).
\[120-8(1+x)\ge 5(2-3x)\]
Expand.
\[120-8-8x\ge 10-15x\]
Simplify \(120-8-8x\) to \(-8x+112\).
\[-8x+112\ge 10-15x\]
Subtract \(10\) from both sides.
\[-8x+112-10\ge -15x\]
Simplify \(-8x+112-10\) to \(-8x+102\).
\[-8x+102\ge -15x\]
Add \(8x\) to both sides.
\[102\ge -15x+8x\]
Simplify \(-15x+8x\) to \(-7x\).
\[102\ge -7x\]
Divide both sides by \(-7\).
\[-\frac{102}{7}\le x\]
Switch sides.
\[x\ge -\frac{102}{7}\]
Decimal Form: -14.571429
x>=-102/7
