# Solving Inequalities Problems

Based in Ypsilanti, Mich., Ainsley Patterson has been a freelance writer since 2007. She especially enjoys utilizing her more than 10 years of craft and sewing experience to write tutorials.Patterson is working on her bachelor's degree in liberal arts at the University of Michigan.Here is a step-by-step guide to how to solve an inequality with a fraction in it.

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Try it risk-free If you can solve linear equations, you can solve linear inequalities.

You should also notice all the processes in the inequality such as multiplication, subtraction, exponents, parentheses and such.

Use the order of operation in reverse to begin to solve the problem.

Solution Let x = the number of subscriptions Leon sells in the last week of the month.

The total number of subscriptions for the month must be greater than 120, so we write : 85 x ≥ 120.We solve the inequality by subtracting 85 from both sides: x ≥ 35.Check To check the answer, we see that 85 35 = 120.Your linear equations might have looked something like these: So, linear inequalities only have variables to the first power and have inequality symbols. Think back to when you last solved a linear equation. If you were given a problem such as x 2 = 6, you most likely looked at it and realized that you need to move the number 2 to the other side of the equation so that your variable is alone.So, you proceeded to subtract 2 from both sides of the equation remembering that to keep an equation equal, whatever you do to one side you also must do to the other.Solving real-world problems that involve inequalities is very much like solving problems that involve equations.In order to get a bonus this month, Leon must sell at least 120 newspaper subscriptions.One easy way to remember the order of operations is to remember the word PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction).Now, when you are solving for a variable, you will use the order of operations in reverse, so instead of beginning with parentheses and ending with addition/subtraction, you will begin with addition/subtraction and end with parentheses.All the properties below are also true for inequalities involving ≥ and ≤.The addition property of inequality says that adding the same number to each side of the inequality produces an equivalent inequality $$If \: x\frac$$ To solve a multi-step inequality you do as you did when solving multi-step equations.

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