Question

I’m having trouble doing this calculus problem from my prep guide Need help

Answer 1

The given inequality is:

`-18\sqrt[]{2x-1}>-36`

To find the solution start by dividing both sides by 18:

`\begin{gathered} \frac{-18\sqrt[]{2x-1}}{18}>-(36)/(18) \\ -\sqrt[]{2x-1}>-2 \end{gathered}`

Now, multiply both sides by -1:

`\begin{gathered} -\sqrt[]{2x-1}\cdot-1>-2\cdot-1 \\ As\text{ we are multiplying by a negative number, reverse the inequality symbol:} \\ \sqrt[]{2x-1}<2 \end{gathered}`

Square both sides:

`\begin{gathered} \sqrt[]{2x-1}^2<2^2 \\ 2x-1<4 \end{gathered}`

Add 1 to both sides:

`\begin{gathered} 2x-1+1<4+1 \\ 2x<5 \end{gathered}`

Divide both sides by 2:

`\begin{gathered} (2x)/(2)<(5)/(2) \\ x<(5)/(2) \\ x<2.5 \end{gathered}`

Also, the number inside the square root can't be negative, then:

`\begin{gathered} 2x-1\ge0 \\ 2x\ge1 \\ x\ge(1)/(2) \\ x\ge0.5 \end{gathered}`

Then 0.5<=x<2.5, in the number line it will be:

The circle in 0.5 is closed and the circle in 2.5 is open.