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

Expression: $\frac{ 4-x }{ 3 }+\frac{ x+1 }{ 4 } \geq 2$

Multiply both sides of the inequality by $12$

$4\left( 4-x \right)+3\left( x+1 \right) \geq 24$

Distribute $4$ through the parentheses

$16-4x+3\left( x+1 \right) \geq 24$

Distribute $3$ through the parentheses

$16-4x+3x+3 \geq 24$

Add the numbers

$19-4x+3x \geq 24$

Collect like terms

$19-x \geq 24$

Move the constant to the right-hand side and change its sign

$-x \geq 24-19$

Subtract the numbers

$-x \geq 5$

Change the signs on both sides of the inequality and flip the inequality sign

$\begin{align*}&x \leq -5 \\&\begin{array} { l }x \in \left\langle-\infty, -5\right]\end{array}\end{align*}$