Question

Solve for x and graph the solution on the number line below. 17 > 3x +5 or 26 < 3x + 5 > Or Inequality Notation: Number Line: -10 -6 4 13

Answer 1

The given expression are :

`17>3x\text{ + 5 or 26}\leq3x+5`

Simplify the first one :

`\begin{gathered} 17>3x\text{ + 5} \\ \text{Subtract 17 from both side :} \\ 17-17>3x+5-17 \\ 0>3x-12 \\ add\text{ 12 on both side :} \\ 0+12>3x-12+12 \\ 12>3x \\ \text{Divide both side by 3 :} \\ (12)/(3)>(3x)/(3) \\ 4>x \end{gathered}`

Now simplify the second one :

`\begin{gathered} 26\leq3x+5 \\ \text{Subtract 5 on both side :} \\ 26-5\leq3x+5-5 \\ 21\leq3x \\ \text{Divide both side by 3 :} \\ (21)/(3)\leq(3x)/(3) \\ 7\leq x \end{gathered}`

So, the x will be :

`\begin{gathered} 4>x\text{ or 7}\leq x \\ \text{ Notation : 4>}x\ge7 \end{gathered}`

To plot on the number line :