How To Solve Inequalities With Variables On Both Sides

Pay special attention to the part where we divide by negative 1. This tutorial provides a great real world application of math.

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Sometimes an inequality will have a variable on both sides of the inequality sign.

How to solve inequalities with variables on both sides. If you think youre looking at a quadratic inequality you may have to FOIL to solve for X. 2x 7 -5x 21 SOLUTION. In this case there is just more to do at the first step.

Multiplying or dividing both sides by a negative number. Variables on both sides. Then solve the inequality by performing the order of operations in reverse.

And then finally to solve our inequality we divide both sides by five which gives us that 𝑥 is less than 16 over five. Multiplying or Dividing a Negative to Solve for Inequalities with Variables on Both Sides. But these things will change direction of the inequality.

See how to turn a word problem into an inequality. 2x - 6 3x - 11. Addition property of inequality.

The solution is also written using interval notation. In this video we go through examples on how to solve inequalities with variables on both sides included special case inequalities. Okay so lets now bring them together to see what our possible values of 𝑥 could be.

Many simple inequalities can be solved by adding subtracting multiplying or dividing both sides until you are left with the variable on its own. Variables on both sides. If youre solving for X and X is on both sides of the inequality you have to move the Xs around and combine then.

Example 1 Solving Inequalities with Variables on Both Sides Solve and graph each inequality. Variables on Both Sides and Dividing By a Negative Number. How Do You Solve a Word Problem Using an Inequality With Variables on Both Sides.

Addition property of inequality. Subtract 10 from both sides. Division property of inequality.

Divide -3 from both sides to isolate the variable. Solve and graph each inequality. Swapping left and right hand sides.

Division property of inequality. Solve a Multiple Step Linear Inequality Variable Both Sides This video provides an example of solving multiple step linear inequalities in one variable with variables on both sides. In this video demonstration I show how to solve an inequality that contains a variable on both sides of the inequality sign.

Were asked to solve for X and we have this compound inequality here negative 16 is less than or equal to 3x plus 5 which is less than or equal to 20 and really theres two ways to approach it which are really the same way and Ill do both of them and Ill actually do both of them simultaneously so one is to just solve this compound inequality all at once and Ill just rewrite it negative 16. -3a 10 -11. Weve solved both inequalities.

A solution to such an inequality is found by transforming the inequality so that the variable is isolated on one side of the inequality. Then express the solution using interval notation. Our next example revisits how to solve equations andor inequalities with variables on both sides.

Solving inequalities with variables on both sides works exactly the same as in equations and as weve already seen. Solving Inequalities in One Variable. Lets take a look at how our new rule applies to solving equations.

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