6th-Solving One-Variable Inequalities Exploration

Equations vs Inequalities The process of solving one-variable inequalities is very similar to solving one-variable equations. The biggest difference between the two is the solution. Let's explore how to solve a one-variable inequality using the steps below. Step 1:Simplify the following inequality using the distributive property and combining like terms.Which of the inequalities below represents this simplified inequality? 2x - 1 < 6x - 1 2x + 1 < 6x - 3 2x - 1 > 6x - 1 2x + 1 > 6x - 3 Step 2: Collect the variables on the right side of the simplified inequality from the problem above. Click the blue dot to enter the correct value for each term of the simplified inequality. 1 4 3 Step 3: Model the Inequality with the Equality Explorer simulation by PhET Select Variables on the Equality Explorer below by double-clicking and model the simplified inequality from step 2 above. Then answer the questions below. To see a quick demonstration for how to use the simulation click here. Step 4: Determine x-values that make your simplified inequality true. Use this button on the Equality Explorer above to help you sort the x-values as True or False. It is True if the x-value creates your simplified inequality from above. It is False if the x-value changes the inequality. True x=2 x=8 x=3 x=5 False x=1 x=0 x=-2 x=-5 What is the solution to the inequality? As you can see from the sorting activity above, there are multiple x-values that make the inequality true. In fact, there are an infinite number of solutions to the inequality. Step 5:Represent the solution.Which of the following represents all the solutions to the inequality? Note: Multiplying or Dividing by a Negative Number In this exploration we did not need to divide or multiply by a negative number. Remember, that if you divide or multiply by a negative number when solving an inequality, you must switch the inequality sign.