Chapter 8.2, Problem 53MR

To determine

To solve:The given inequality for $y$ and then graph the inequality.

Answer to Problem 53MR

The solution of inequality $4x+5y\ge 10$ for y is $y\ge 2-0.8x$ , and the graph of inequality $y\ge 2-0.8x$ is shown in Figure-1.

Explanation of Solution

Given information:

The given system of inequality is $4x+5y\ge 10$

Concept used:

Adding, subtracting, multiplying and dividing by a positive quantity on each side does not change thesign of an inequality.

Calculations:

The given inequality is $4x+5y\ge 10$ ,

  $\Rightarrow 4x-4x+5y\ge 10-4x$  Subtracting 4x from each side $\Rightarrow \cancel{4x}-\cancel{4x}+5y\ge 10-4x$

  $\Rightarrow 5y\ge 10-4x$

  $\Rightarrow \frac{5y}{5}\ge \frac{10-4x}{5}$  Dividing each side by 5

  $\Rightarrow y\ge 2-0.8x$

Thus, the solution of inequality $4x+5y\ge 10$ for y is $y\ge 2-0.8x$ .

The graph of inequality $y\ge 2-0.8x$ is shown in Figure-1 here.

  

Interpretation: All the points of the shaded region are the solutions of inequality $y\ge 2-0.8x$ .

Conclusion:

The solution of inequality $4x+5y\ge 10$ for y is $y\ge 2-0.8x$ , and the graph of inequality $y\ge 2-0.8x$ is shown in Figure-1.