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How to Solve Inequalities Using Division

Solving inequalities is much like solving standard equations. To isolate the variable you must add, subtract, multiply and sometimes divide. You may divide the inequality by any number, provided that you perform the division on both sides, just as you do to solve equalities. The only difference is that when you divide each side of an inequality by a negative number, you must flip the sign to maintain the validity of the equation.

Instructions

    • 1

      Simplify each side of the equation by performing any operations requiring the distributive property, exponents, multiplication, division, addition or subtraction. Remember to observe the order of operations according to the acronym PEMDAS: parentheses, exponents, multiplication, division and then addition and subtraction.

      For instance, both sides of the equation -3(x + 2) > 5^2 - 4 can be further simplified. Use the distributive property to simplify the left hand side to -3x - 6. On the right, simplify the exponent first, then subtract. The final equation looks like this: -3x - 6 > 21.

    • 2

      Add or subtract as needed to isolate the variable on one side.

      In the equation -3x - 6 > 21, add 6 to both sides to get -3x > 27.

    • 3

      Divide both sides by the variable's coefficient to isolate it on one side of the equation.

      For example, -3x > 27 becomes x > -9.

    • 4

      Determine which way the inequality sign should face. If the number you divided by in the last step was positive, leave the sign how it is. If it was negative, flip the sign.

      For example, in the last step you divided by -3. Since this was a negative number, you must flip the sign. The solution to the problem is x < -9.

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