# Algebra Problem Set: Inequalities, Absolute Value

66. Young's rule for determining the amount of a medicine dosage for a child is given by C = where a is the child's age and ad is the usual adult dosage, in milligrams. The dosage of a medication for a 5 year old child must stay between 50mg and 100 mg. Find the equivalent adult dosage.

52. 2|2x - 7| + 11 = 25

106. | | ≥ 1

38. -4 ≤ ≤ 4

58. < -4 or > 4

88. |5x + 2| ≤ 13

90. |7 - 2y| > 5

44. 4y - 3x ≥ -12 equation (1)

4y + 3x ≥ -36. equation (2)

y ≤ 0, equation (3)

x ≤ 0 equation (4)

***See attached file.***

## Solution This solution is **FREE** courtesy of BrainMass!

66. Young's rule for determining the amount of a medicine dosage for a child is given by

C = where a is the child's age and ad is the usual adult dosage, in milligrams

The dosage of a medication for a 5 year old child must stay between 50mg and 100 mg. Find the equivalent adult dosage.

A= 5

So the adult dosage is between 170 mg and 340 mg.

52. 2|2x - 7| + 11 = 25

When , , the equation can be simplified as

When , the equation is

So the solution is x = 0 or x = 7.

106. | | ≥ 1

It can be rewritten as

For

For

So the solution is

This can also be written as: (-∞, -1] U [7/2, ∞) or {x | x ≤ -1 or x ≥ 7/3}.

38. -4 ≤ ≤ 4

, 9

The interval notation for this answer is [-13/3, 9]. The set notation is {x | -13/3 ≤ x ≤ 9}.

To draw this on a number line put closed dots at the points -13/3 and 9 (closed dots because of the ≤ signs), then shade the line in between the dots.

58. < -4 or > 4

or

or

In interval notation, the answer is: In set notation, this looks like: {x | x < -13/3 or x > 9}. The graph would have open dots at -13/3 and 9, with shading to the left of -13/3 and to the right of 9.

88. |5x + 2| ≤ 13

[ -3, ]

90. |7 - 2y| > 5

or

y > 6 or y < 1

44. 4y - 3x ≥ -12 equation (1)

4y + 3x ≥ -36. equation (2)

y ≤ 0, equation (3)

x ≤ 0 equation (4)

Equation (1)

Equation (2)

Substitute this into equation (1).

One of the vertices is (-8, -3).

The vertex on the right is formed by intersecting equation (1) and equation (3).

its y-coordinate is 0. Therefore, the second vertex is at (-4, 0).

The vertex on the left is formed by intersecting equation (2) and equation (3).

its y-coordinate is 0. Therefore, the second vertex is at (-12, 0).

Therefore, the three vertices are (-8, -3), (-4, 0), and (-12, 0).