Question

solve the inequality (2>2x + 5). graph the solution on a number - line and represent the solution in interval notation when possible. choose the correct graph of the solution. a. b. the solution is all real numbers c. there is no solution. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution written in interval notation is b. there is no solution. it is not possible to write interval notation

Explanation:

Step1: Solve the inequality

Subtract 5 from both sides of $2>2x + 5$. We get $2-5>2x$, which simplifies to $- 3>2x$. Then divide both sides by 2, so $x<-\frac{3}{2}$.

Step2: Write in interval - notation

The interval - notation for $x<-\frac{3}{2}$ is $(-\infty,-\frac{3}{2})$.

Step3: Determine the graph

The graph of $x<-\frac{3}{2}$ is a number line with an open circle at $-\frac{3}{2}$ (because the inequality is strict, $x$ cannot equal $-\frac{3}{2}$) and an arrow pointing to the left.

Answer:

The solution written in interval notation is $(-\infty,-\frac{3}{2})$. The correct graph is the one with an open - circle at $-\frac{3}{2}$ and an arrow pointing to the left. (Based on the given graphs, you need to identify the one that matches this description).