Question

Solve and graph the solutions to the inequalities below using any of the method from class: a table, a graph,"undoing," or algebraic operations.(You may need to use a separate sheet of notebook paper or graph paper.)Solve item c.

Answer 1

x > 2

EXPLANATION :

From the problem, we have the inequality :

`3<4x-5`

Solve for x :

Put the terms with variables on the left side and the constants to the right side.

Subtract 4x from both sides :

`\begin{gathered} 3-4x<\cancel{4x}-5-\cancel{4x} \\ 3-4x<-5 \end{gathered}`

Subtract 3 from both sides :

`\begin{gathered} \cancel{3}-4x-\cancel{3}<-5-3 \\ -4x<-8 \end{gathered}`

Divide both sides by -4.

Take note that if you divide a negative number from the inequality, the symbol will change.

So from "<", it will become ">"

`\begin{gathered} \frac{\cancel{-4}x}{\cancel{-4}}<(-8)/(-4) \\ x>2 \end{gathered}`

The solution is x > 2

The graph will be :

The boundary line is a dashed type since the symbol is ">" and the region is to the right of x = 2