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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.

7 Graph Both Of The Linear Inequalities And Shade In The Possible Solutions Usef As The Yaxis And C As TheXaxisThis Has Already Been Started For You But There I class=

Sagot :

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

[tex]c+f\ge50[/tex]

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;

[tex]x+y\ge50[/tex]

In slope-intercept form, this is written as;

[tex]y\ge-x+50[/tex]

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

[tex]f\ge-c+50[/tex]

The other inequality is written out as

[tex]2c+5f\le175[/tex]

In slope-intercept form, this becomes;

[tex]\begin{gathered} 5f\le-2c+175 \\ \text{Divide both sides by 5} \\ \frac{5f}{5}\le-\frac{2c+175}{5} \\ f\le-\frac{2c}{5}+\frac{175}{5} \\ f\le-\frac{2c}{5}+35 \\ f\le-\frac{2}{5}c+35 \end{gathered}[/tex]

We can now graph both inequalities as follows;

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

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

View image AdamaryE475136
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