Question

Solve the given inequality and graph the solution on a number line

Answer 1

`-(x)/(2)+(3)/(2)<(5)/(2)`

Subtracting 3/2 at both sides of the inequality:

`\begin{gathered} -(x)/(2)+(3)/(2)-(3)/(2)<(5)/(2)-(3)/(2) \\ -(x)/(2)<1 \end{gathered}`

Multiplying by 2 at both sides of the inequality:

`\begin{gathered} -(x)/(2)\cdot2<1\cdot2 \\ -x<2 \end{gathered}`

Dividing by -1 at both sides of the inequality:

`\begin{gathered} (-x)/(-1)<(2)/(-1) \\ x>-2 \end{gathered}`

(Dividing by a negative number changes the inequality symbol)

This solution is represented on the number line as follows:

Notice that -2 is not included in the solution.