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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| &#8804; 13

90. |7 - 2y| > 5

44. 4y - 3x &#8805; -12 equation (1)
4y + 3x &#8805; -36. equation (2)
y &#8804; 0, equation (3)
x &#8804; 0 equation (4)

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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. | | &#8805; 1

It can be rewritten as

For

For

So the solution is

This can also be written as: (-&#8734;, -1] U [7/2, &#8734;) or {x | x &#8804; -1 or x &#8805; 7/3}.

38. -4 &#8804; &#8804; 4

, 9

The interval notation for this answer is [-13/3, 9]. The set notation is {x | -13/3 &#8804; x &#8804; 9}.

To draw this on a number line put closed dots at the points -13/3 and 9 (closed dots because of the &#8804; 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| &#8804; 13

[ -3, ]

90. |7 - 2y| > 5

or

y > 6 or y < 1

44. 4y - 3x &#8805; -12 equation (1)
4y + 3x &#8805; -36. equation (2)
y &#8804; 0, equation (3)
x &#8804; 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).

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