By LearningExpress Editors
Updated on Oct 3, 2011
To review these concepts, go to Algebraic Inequalities Study Guide.
Algebraic Inequalities Practice Questions
Problems
Practice 1
Solve each inequality for x. Show the solution on a number line with values from –10 to 10.
 6x + 11 < 29
 8 –7x > 50
 3x – 6 < 0
 –4x + 7 ≤ 19
Practice 2
Solve each compound inequality for x. Show the solution on a number line with values from –10 to 10.
 0 < x – 4 ≤ 4
 49 > –7x > –21
 –13≤ 3x–7< 20
Practice 3
Solve each inequality for y in terms of x.
 y – 4 > x
 8y –2x ≤ 24
 15x – 5y > 100
Solutions
Practice 1
1.  Subtract 11 from both sides of the inequality and divide by 6: 


Because x is less than 3, 3 is not part of the solution set. Draw a hollow circle around 3 and shade to the left, where values are less than 3:  
2.  Multiply both sides of the inequality by 4: 


Because x is greater than or equal to –8, –8 is part of the solution set. Draw a closed circle around –8 and shade to the right, where values are greater than –8:  
3.  Subtract 8 from both sides of the inequality and divide by –7. Because we are dividing by a negative number, change the inequality symbol from greater than to less than: 


Because x is less than –6, –6 is not part of the solution set. Draw a hollow circle around –6 and shade to the left, where values are less than –6:  
4.  Add 6 to both sides of the inequality and divide by 3: 


Because x is less than 2, 2 is not part of the solution set. Draw a hollow circle around 2 and shade to the left, where values are less than 2:  
5.  Subtract 7 from both sides of the inequality and divide by –4. Because we are dividing by a negative number, change the inequality symbol from less than or equal to greater than or equal: 


Because x is greater than or equal to –3, –3 is part of the solution set. Draw a closed circle around –3 and shade to the right, where values are greater than –3:  


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From Algebra in 15 Minutues A Day. Copyright © 2009 by LearningExpress, LLC. All Rights Reserved.
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