Question

How to solve one of these - im very confused :(

Answer 1

The graph represents the inequality:

`x<-3`

The reason we used strictly less than (<) is that the circle is not shaded. Therefore, the correct inequality has to be either the first or last.

We will simplify the inequalities to see which one is equivalent.

First Inequality:

`5(4x+3)<10(2x+1)+7`

Expanding the brackets using the distributive property, we have:

`\begin{gathered} 20x+15<20x+10+7_{} \\ 20x+15<20x+17 \end{gathered}`

Subtracting 20x from both sides, we have:

`\begin{gathered} 20x+15-20x<20x+17<20x \\ 15<17 \end{gathered}`

This is not the inequality.

Last Inequality:

`3x+10>5x+16`

Subtract 5x from both sides:

`\begin{gathered} 3x+10-5x>5x+16-5x \\ -2x+10>16 \end{gathered}`

Subtract 10 from both sides:

`\begin{gathered} -2x+10-10>16-10 \\ -2x>6 \end{gathered}`

Divide both sides by -2. Dividing by a negative number will reverse the sign:

`\begin{gathered} (-2x)/(-2)>(6)/(-2) \\ x<-3 \end{gathered}`

Hence, this is the inequality.

ANSWER: The correct inequality is

`3x+10>5x+16`