Solve the compound inequality and graph the solution sets. $2 x - 1 \geq 5 \text { and } x 0$

Question

Solve the compound inequality and graph the solution sets. $2 x - 1 \geq 5 \text { and } x > 0$

Quizplus · Accepted Answer

Firstly, solving for $x$ in the first inequality, we get $2x-1 \geq 5 \implies 2x \geq 6 \implies x \geq 3$. The second inequality tells us that $x > 0$. Therefore, our final solution set is $\boxed{[3, \infty)}$.

To graph this solution set: 
- We plot a solid dot at $x=3$ because it is included in the solution set. 
- We then draw a shaded line to the right of $x=3$ to represent all the values greater than 3 which are also included in our solution set. 
- Since $x=0$ is not included in the solution set, we draw an open circle at $x=0$ and do not include it in our shaded region.

The resulting graph should match choice C.

Solve the Compound Inequality and Graph the Solution Sets 2x−1≥5 and x>02 x - 1 \geq 5 \text { and } x > 02x−1≥5 and x>0

Solve the Compound Inequality and Graph the Solution Sets $2 x - 1 \geq 5 \text { and } x > 0$