Question

7. Graph both of the linear inequalities and shade in the possible solutions. (Usef as the y-axis and c as theX-axis.)This has already been started for you, but there is more to do.Hint: It may help to write the inequalities in slope-intercept form first.

Answer 1

From the information provided, the inequality representing the combination of codebooks and flashlights is

`c+f\ge50`

The variable f represents the y variable while the variable c reprsents the x variable. In other words, what we have here could also be written as;

`x+y\ge50`

In slope-intercept form, this is written as;

`y\ge-x+50`

Therefore, the inequality here would be expressed in slope-intercept form as;

`f\ge-c+50`

The other inequality is written out as

`2c+5f\le175`

In slope-intercept form, this becomes;

`\begin{gathered} 5f\le-2c+175 \\ \text{Divide both sides by 5} \\ (5f)/(5)\le-(2c+175)/(5) \\ f\le-(2c)/(5)+(175)/(5) \\ f\le-(2c)/(5)+35 \\ f\le-(2)/(5)c+35 \end{gathered}`

We can now graph both inequalities as follows;

`\begin{gathered} \text{Note that the green region represents the inequality,} \\ f\ge-c+50 \end{gathered}`
`\begin{gathered} \text{Also the purple region represents the inequality,} \\ f\le-(2)/(5)c+35 \end{gathered}`

The possible solutions for both inequalities is represented by the region where both colors intersect.