#Solutions of equations and inequalities equation systems free
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To solve this, we want to divide both sides of this equation by -8.įreerolls. To show you what that means, we'll solve an equality and an inequality using the rules of equation solving and inequality solving. It's clear with these numbers that reversing the inequality is essential when you are mutliplying both sides of the inequality or dividing both sides of the inequality by a negative number.įailure to do this will get you the wrong answer as you will find out when you confirm the results of your solution. You needed to do that to preserve the inequality. The inequality started as less than and became greater than because you were dividing both sides of the inequality by a negative number. 25 / -5 = 5 on the right side of the inequality. 35 / -5 = 7 on the left side of the inequality. The second example is simply the reverse of the first example and starts with:ĭivide both sides of this inequality by -5 and you get: It is also clear to see that -35 is less than -25. It's clear to see that 7 really is greater than 5. The inequality started as greater than and became smaller than because you were multiplying both sides of the inequality by a negative number. Multiply both sides of that inequality by -5 and you get:ħ*-5 = -35 on the left side of the inequality.ĥ*-5 = -25 on the right side of the inequality. The first example will be multiplication. The following examples will show this rule in action. If you multiply or divide an inequality by a negative number, then the inequality reverses. The difference between solving equations and solving inequalities is: If you multiply or divide one side of an equation or inequality by the same number, you have to multiply or divide the other side of the equation or inequality by the same number. If you add or subtract a number to one side of an equation or inequality, you have to add or subtract the same number to the other side of the equation or inequality. Whatever you do to one side of the inequality, you have to do to the other side to preserve the inequality. The technique for solving inequalities is: Whatever you do to one side of the equation, you have to do to the other side to preserve the equality Solving Inequalities is very similar to solving Equations.
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