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Linear Inequalities

Long Answer Type

81. Find the linear inequalities for which the shaded area in the given graph is the solution set:

Consider the line 2x + y = 2. Clearly, the shaded portion and the origin are on the opposite sides of the graph. So, we have its inequality as:
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Now, consider the line x + 2y = 8.
Origin and shaded region are on the same side of the line x + 2y = 8.
So, its inequality is:
$box enclose straight x plus 2 straight y less or equal than 8 end enclose$ [∵ 0 + 2(0) ≤ 8 is true]
Finally, consider the line x - y = 1
Origin and shaded region are on the same side.
So, its inequality is:
$box enclose straight x minus straight y less or equal than 1 end enclose$ [∵ 0 - 0 ≤ 1 is true]
Also, x ≥ 0 and y ≥ 0
Thus, the linear inequalities are:
2x + y ≥ 2, x + 2y ≤ 8, x - y ≤ 1, x ≥ 0 and y ≥ 0

391 Views

82.

Solving the following inequalities. Also represent the solutions on the number line.
3x - 2 > x + 5

162 Views

Short Answer Type

83.

Solving the following inequalities. Also represent the solutions on the number line.
-4x + 1 ≤ 2 (1 - x)

143 Views

84.

Solving the following inequalities. Also represent the solutions on the number line.
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135 Views

85.

Solving the following inequality. Also represent the solutions on the number line.
$straight x less than open parentheses fraction numerator 2 straight x plus 1 over denominator 3 end fraction close parentheses minus open parentheses fraction numerator 5 straight x minus 1 over denominator 2 end fraction close parentheses$

119 Views

86.

Solve x + 1 < 8 - x, where
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