Question

Watch the video and then solve the problem given below.Click here to watch the video.Solve the inequality both algebraically and graphically. Give the solution in interval notation and draw it on a number line graph.x−54

Answer 1

Given the inequality below:

`(x-5)/(4)<(9)/(5)`

Solving algebraically as shown below:

`\begin{gathered} (x-5)/(4)<(9)/(5) \\ \text{Lcm of the denominator(4 and 5) is 20} \\ \text{mltiply through by the Lcm(20)} \\ 20*((x-5))/(4)<20*(9)/(5) \end{gathered}`
`\begin{gathered} 5(x-5)<4*9 \\ 5x-25<36 \\ 5x<36+25 \\ 5x<61 \\ x<(61)/(5) \\ x<12.2 \end{gathered}`

Solving graphically as shown below the plotting of x < 12.2

The number line graph is the number line showing x < 61/5, as shown below:

The interval notation of the solution is (- ∞, 61/5) or (- ∞, 12.2)