Algebra 1
Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 5.1, Problem 55HP
To determine

Write the process of solving and linear graphing.

Expert Solution & Answer
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Answer to Problem 55HP

Explanation of Solution

Concept Used:

Rules for solving inequality equations:

These things do not affect the direction of the inequality:

  • Add (or subtract) a number from both sides
  • Multiply (or divide) both sides by a positive number
  • Simplify a side

But these things do change the direction of the inequality (" < " becomes " > " for example):

  • Multiply (or divide) both sides by a negative number
  • Swapping left and right hand sides

For Inequality equation: If b>c  ⇒  c  <  b  or  b  <  c  ⇒  c  >  b

Example:

    Steps Explanation
    2x+14≤242x+14−14≤24−142x≤102x2≤102 x≤5Original equation Subtract 14 from both sides. Divide each side by 2 Solution:

      (  −∞  ,  5  ]

    7x−5>8x7x−7x−5>8x−7x−5>x  or  x  <  −5Original Equation Subtract 7x from both sides.

      [  Rule  b>c  ,  then  c<b  ] Solution:

      x  <  −5 or

      (  −∞  ,  5  )

Here is a summary of how to graph inequalities:

1) Draw a number line.2) Put either an open circle or a closed dot above the number given.

For ≤ and ≥ , use a closed dot to indicate the number itself is part of the solution.

For < and >, use an open circle to indicate the number itself is not part of the solution.

3) Choose which way the arrow should go. Either think about which numbers would be part of the solution. Or, as long as the variable is listed first, you can just look at the symbol

For ≤ and <, the arrow points down to the left.

For ≥ and >, the arrow points up to the right.

    Plotting inequalities: To plot an inequality:

    Such as x>3, on a number line, first draw a circle over the number (e.g., 3).

    Then if the sign includes equal to (= or =), fill in the circle (solid circle).

    If the sign does not include equal to (> or <), leave the circle (hollow circle) unfilled in.

    For x < 3 or x >3, there is a hollow circle.

    For x≤3    or    x≥3 , there is a solid circle.

    		Algebra 1, Chapter 5.1, Problem 55HP

Thus, solving linear inequalities is similar to solving linear equations. You must isolate the variable on one side of the inequality.

To graph, if the problem is a less than or a greater than inequality, an open circle is used. Otherwise a dot is used.

If the variable is on the left hand side of the inequality, and the inequality sign is less than (or less than or equal to), the graph extends to the left; otherwise it extends to the right.

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Chapter 5 Solutions

Algebra 1

Ch. 5.1 - Prob. 1ACYPCh. 5.1 - Prob. 1BCYPCh. 5.1 - Prob. 2CYPCh. 5.1 - Prob. 3ACYPCh. 5.1 - Prob. 3BCYPCh. 5.1 - Prob. 4CYPCh. 5.1 - Prob. 1CYUCh. 5.1 - Prob. 2CYUCh. 5.1 - Prob. 3CYUCh. 5.1 - Prob. 4CYU
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Prob. 46STPCh. 5.4 - Prob. 47STPCh. 5.4 - Prob. 48SRCh. 5.4 - Prob. 49SRCh. 5.4 - Prob. 50SRCh. 5.4 - Prob. 51SRCh. 5.4 - Prob. 52SRCh. 5.4 - Prob. 53SRCh. 5.4 - Prob. 54SRCh. 5.4 - Prob. 55SRCh. 5.4 - Prob. 56SRCh. 5.4 - Prob. 57SRCh. 5.4 - Prob. 58SRCh. 5.4 - Prob. 59SRCh. 5.4 - Prob. 60SRCh. 5.4 - Prob. 61SRCh. 5.4 - Prob. 62SRCh. 5.4 - Prob. 63SRCh. 5.4 - Prob. 64SCh. 5.4 - Prob. 65SCh. 5.4 - Prob. 66SCh. 5.4 - Prob. 67SCh. 5.4 - Prob. 68SCh. 5.4 - Prob. 69SCh. 5.4 - Prob. 70SCh. 5.4 - Prob. 71SCh. 5.4 - Prob. 72SCh. 5.5 - Prob. 1BCYPCh. 5.5 - Prob. 2CYPCh. 5.5 - Prob. 3ACYPCh. 5.5 - Prob. 3BCYPCh. 5.5 - Prob. 20PPSCh. 5.5 - Prob. 24PPSCh. 5.5 - Prob. 25PPSCh. 5.5 - Prob. 26PPSCh. 5.5 - Prob. 27PPSCh. 5.5 - Prob. 28PPSCh. 5.5 - Prob. 29PPSCh. 5.5 - Prob. 32PPSCh. 5.5 - Prob. 33PPSCh. 5.5 - Prob. 34PPSCh. 5.5 - Prob. 35PPSCh. 5.5 - Prob. 36PPSCh. 5.5 - Prob. 37PPSCh. 5.5 - Prob. 38PPSCh. 5.5 - Prob. 39PPSCh. 5.5 - Prob. 40PPSCh. 5.5 - Prob. 41PPSCh. 5.5 - Prob. 43HPCh. 5.5 - Prob. 44HPCh. 5.5 - Prob. 45HPCh. 5.5 - Prob. 1ACYPCh. 5.5 - Prob. 1CYUCh. 5.5 - Prob. 2CYUCh. 5.5 - Prob. 3CYUCh. 5.5 - Prob. 4CYUCh. 5.5 - Prob. 5CYUCh. 5.5 - Prob. 6CYUCh. 5.5 - Prob. 7CYUCh. 5.5 - Prob. 8PPSCh. 5.5 - Prob. 9PPSCh. 5.5 - Prob. 10PPSCh. 5.5 - Prob. 11PPSCh. 5.5 - Prob. 12PPSCh. 5.5 - Prob. 13PPSCh. 5.5 - Prob. 14PPSCh. 5.5 - Prob. 15PPSCh. 5.5 - Prob. 16PPSCh. 5.5 - Prob. 17PPSCh. 5.5 - Prob. 18PPSCh. 5.5 - Prob. 19PPSCh. 5.5 - Prob. 21PPSCh. 5.5 - Prob. 22PPSCh. 5.5 - Prob. 23PPSCh. 5.5 - Prob. 30PPSCh. 5.5 - Prob. 31PPSCh. 5.5 - Prob. 42PPSCh. 5.5 - Prob. 46HPCh. 5.5 - Prob. 47HPCh. 5.5 - Prob. 48STPCh. 5.5 - Prob. 49STPCh. 5.5 - Prob. 50STPCh. 5.5 - Prob. 51STPCh. 5.5 - Prob. 52SRCh. 5.5 - Prob. 53SRCh. 5.5 - Prob. 54SRCh. 5.5 - Prob. 55SRCh. 5.5 - Prob. 56SRCh. 5.5 - Prob. 57SRCh. 5.5 - Prob. 58SRCh. 5.5 - Prob. 59SRCh. 5.5 - Prob. 60SRCh. 5.5 - Prob. 61SCh. 5.5 - Prob. 62SCh. 5.5 - Prob. 63SCh. 5.5 - Prob. 64SCh. 5.5 - Prob. 65SCh. 5.5 - Prob. 66SCh. 5.5 - Prob. 67SCh. 5.5 - Prob. 68SCh. 5.6 - 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