Question

Write the inequality shown by the shaded region in the graph with the boundary line 2x + 2y = -6.

Answer 1

Inequalities are used to describe unequal expressions.

The inequality of the shaded region is: $\mathbf{y + x> -3 }$

The boundary line is given as:

$\mathbf{2x + 2y = -6}$

Divide through by 2

$\mathbf{x + y = -3}$

Make y the subject

$\mathbf{y = -3 - x}$

The shaded region is above the boundary line (see attachment)

This means that, we make use of the greater than sign (>)

So, we replace = with >

$\mathbf{y > -3 - x}$

As a standard form, we have:

$\mathbf{y + x> -3 }$

Hence, the inequality of the shaded region is: $\mathbf{y + x> -3 }$

Read more about inequalities at:

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