Solve and graph the solution set: $- 1 3 x + 5 \geq - 4$

Question

Solve and graph the solution set: $- 1 > 3 x + 5 \geq - 4$

Quizplus · Accepted Answer

Starting with the left side of the inequality: \begin{align*} -1 &> 3x + 5 \ -6 &> 3x \ -2 &> x \ x &< -2 \end{align*} Moving on to the right side of the inequality: \begin{align*} 3x + 5 &\geq -4 \ 3x &\geq -9 \ x &\geq -3 \end{align*} Putting it all together, the solution is: $$x < -2 \text{ or } x \geq -3$$ This can be graphed on a number line as: \begin{tikzpicture} \draw[thick, <->] (-5,0) -- (2,0) node[below]{$x$}; \draw[-o] (-2,0) node[above]{$-2$} -- (-5,0); \draw[fill=white] (-2,0) circle [radius=0.1]; \draw[thick,-o] (-3,0) node[above]{$-3$} -- (-2,0); \draw[fill=white] (-3,0) circle [radius=0.1]; \draw[thick, ->] (2,0) -- ++(0.5,0) node[below]{$+$}; \end{tikzpicture}

Solve and Graph the Solution Set −1>3x+5≥−4- 1 > 3 x + 5 \geq - 4−1>3x+5≥−4

Solve and Graph the Solution Set $- 1 > 3 x + 5 \geq - 4$