$4\left( 4-x \right)+3\left( x+1 \right) \geq 24$
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$\begin{align*}&x \leq -5 \\&\begin{array} { l }x \in \left\langle-\infty, -5\right]\end{array}\end{align*}$