Question

Which is the best interpretation of the solution set for the compound inequality? 3/2x-1-10 Ox

Answer 1

Could you please provide an inamge for the compound inequality?

Weare given four inequalities and have to find which one has no solution:

1)

`\begin{gathered} x>2 \\ \text{and} \\ 3x\leq9\Rightarrow x\leq3 \end{gathered}`

so,this one has solutions since x can be larger than 2 and smaller or equal to 3, like in the case of x = 2.5

2)

`\begin{gathered} x>1 \\ \text{and} \\ 2x\leq-2\Rightarrow x\leq-1 \end{gathered}`

this one has NO solution, since the x values smaller than or equal to negative one cannot be at the same time larger than 1.

3)

`\begin{gathered} x>-1 \\ \text{and} \\ 4x\ge-8\Rightarrow x\ge-2 \end{gathered}`

this one has solution and that is x>-1

4)

`\begin{gathered} x>-2 \\ \text{and} \\ 5x\ge15\Rightarrow x\ge3 \end{gathered}`

this one also has solution: x >= 3

Therefore, the only one with no solution is the second one provided.