Question

Would like to know how to solve step by step I have no idea what to do here

Answer 1

So first of all let's rewrite the inequalities. The first one is:

`1.5x-1>6.5`

We can add 1 at both sides of it:

`\begin{gathered} 1.5x-1+1>6.5+1 \\ 1.5x>7.5 \end{gathered}`

And we can divide both sides by 1.5:

`\begin{gathered} (1.5x)/(1.5)>(7.5)/(1.5) \\ x>5 \end{gathered}`

So this inequality can be written as x>5. The second one is:

`7x+3<-25`

We substract 3 from both sides:

`\begin{gathered} 7x+3-3<-25-3 \\ 7x<-28 \end{gathered}`

And we divide both sides by 7:

`\begin{gathered} (7x)/(7)<-(28)/(7) \\ x<-4 \end{gathered}`

So the inequalities are x>5 and x<-4. This means that the parts of the number line that must be colored are those at the right of 5 (according to the first inequality) and at the left of -4 (according to the second). Since the inequalities use the siymbols "smaller than" and "greater than" with no equals there must be blank dots at -4 and 5. The option that meets all these conditions is the second which is the answer.