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Solving Linear Equations and Inequalities in One Variable

HSA-REI.B.3
Answer Keys Here

Aligned To Common Core Standard:

High School - HSA-REI.B.3

How To Solve Linear Equations and Inequalities - Solving linear equations in itself is a tough task, but adding inequalities in the mix can only make the whole thing more complicated. However, it is not that complicated, so let’s learn sequentially how we can solve such problems. Let us consider an example where we can solve the equation comprising of both equations and inequalities. -2(x - 3) < 5( x + 1) - 12 By the looks of it, you must think this a tough problem to solve. However, it is not that tough to answer, let's solve it manually. -2(x - 3) < 5(x + 1) - 12 Let us open the brackets by multiplying the outside numbers with the terms inside the parenthesis. -2x+6<5x+5-12 Now, we add and subtract similar terms on each side of inequality sign (if present): -2x + 6 < 5x - 7 Now, we place the variable terms on the left side of the equation and constant terms on the right side. -2x - 5x < -7 + 6, -7x < -13 Now, we divide the whole equation by – 7, and then we will get the answer: -7x / (-7) < -13 / (-7), x< 13/7 By this answer, we conclude that the value of x must be less than 13/7. This awesome series of worksheets and independent lessons for students will help you learn how to solve inequalities or linear equations that have a single unknown variable present.

Printable Worksheets And Lessons






Homework Sheets

I forgot how difficult some of these problems appear to kids that see them for the first time.

  • Homework 1 - We have like terms, or terms that have the same variables raised to the same powers. To subtract like terms, subtract their coefficients.
  • Homework 2 - Use inverse operations to isolate the variable.
  • Homework 3 - When working on operations in the inequality, be sure to do the same operation to both sides of the inequality.



Practice Worksheets

I find that if I encourage kids to number their steps when answering these questions, they have an easy time.

  • Practice 1 - We have to solve for a variable, use inverse operations to undo the operations in the equation. Be sure to do the same operation to both sides of the equation.
  • Practice 2 - Follow each of these problems all the way through and solve for x or a as needed.
  • Practice 3 - Solve for 11a - 3a - 2 = 5.



Math Skill Quizzes

Combine the like terms first when tackling these.

  • Quiz 1 - Solve following linear inequalities.
  • Quiz 2 - Wow, this a real mix of problems.
  • Quiz 3 - What is n in the equation: 13n + 9n – 32 = 11