Inequalities With Negative Numbers

B x9 0 x 9 0 Show Solution. If you multiple or divide the compound inequality by a negative number you will need to flip all the inequality signs.

Inequalities One And Two Step With Negatives Color By Number Math Review Activities Fun Math Activities Teaching Math

The product of two negative numbers becomes larger than either of the original numbers.

Inequalities with negative numbers. If p q and d is negative then pd qd inequality swaps. Therefore in this case there is no solution since it is impossible for an absolute value to be strictly less than zero ie. Dont forget that if you multiply or divide by a negative number you MUST flip the sign of the inequality.

Our summary above is actually a mathematical theorem. Subtract 4 4 4 from both sides. Level 4-5 GCSE Maths Revision Cards 252 Reviews 899 View Product.

And we are doing that. So let us swap them over and make sure the inequalities point correctly. It is a very easy proof so I suppose that you would be able to understand it.

X 9 x. Graphing Inequalities 6 RTF. We still cant have absolute value be less than zero however it can be equal to zero.

Anytime you multiply or divide both sides of the inequality you must flip or change the direction of the inequality sign. So since weve divided by negative 4 the rules of inequalities state we must flip the inequality symbol. Lets try another example of solving inequalities with negatives.

The proof of this is shown below. The two inequalities x2 x and x 1 are not the same. If you multiply both p and q by a negative number the inequality swaps.

Notice that a. Thats one of the big differences between solving equalities and solving inequalities. If we multiply or divide an inequality by a negative number then the sign of the inequality becomes reversed.

If you multiply numbers p and q by a positive number there is no change in inequality. This set features two-step addition and subtraction inequalities such as 2x 5 15 and 4x -2 14. The same rule would apply if youre multiplying both sides by a fraction.

Thats why when multiplied by a negative number the larger of the two values will be less than the smaller of the two values. If we perform any basic operation to. 36x9.

6 x 3 And that is the solution. Solving an inequality for a variable. But when we multiply both a and b by a negative number the inequality swaps over.

Solving inequalities is the same as solving equations. Graphing Inequalities Workheet 6 - Here is a 12 problem worksheet where students will both solve inequalities and graph inequalities on a number line. That is if and are real numbers and then.

In the following example notice how the sign becomes a sign when the inequality is divided by -2 -2x - 10 2 -2x - 10 10 2 10 -2x 12 x -6 Dividing by -2 required the flipping of the inequality sign. When we multiply both a and b by a positive number the inequality stays the same. Now I didnt draw the inequality here because we have to remember if we multiply or divide both sides of an inequality by a negative number you have to flip the inequality.

Multiplyingdividing by the same NEGATIVE number on both sides AND changing the orientation of the inequality sign. Given any set of positive or negative numbers the one further to the left on the number line is the smallest. Summarizing multiplying an inequality by a negative number is the same as reversing their order on the number line.

But in fact we cannot do this. Whenever you multiply or divide an inequality by a negative number you must flip the inequality sign. We are multiplying both sides by negative 15 which is.

If a b and c is positive then ac bc. 2 x 4 6 -2x4geq-6 2 x 4 6. But to be neat it is better to have the smaller number on the left larger on the right.

Since youre dividing by a negative number you need to flip the inequality sign. But in the inequality x2 x we have to take into account the possibility that x is negative since if x is negative x2 which must be positive or zero is always greater than x. Graphing Inequalities 6 PDF.

We divided by -2 on both sides and switched to. Operations in inequalities differ from equations because certain operations will cause the greater than or less than sign to flip. When both sides of an inequality are multiplied by a negative value the direction of the inequality is reversed.

Because we are multiplying by a negative number the inequalities change direction. P. -7x 21 -7 -7 x -3 2 You will graph your solutions.

There are only 2 things you need to know 1 If you multiply or divide by a negative number you must switch the sign. Problem inequality solve set builder notation. Dividing by a negative means switch the sign.

This is almost the same as the previous part. Just perform the order of operations in reverse. Now divide both sides of the inequality by 3.

3_x_ 3 6 3 x 2. If p q and d is positive then pd qd. We divided by 2 on both sides.

This sounds harmless enough. The inequality -2x 4 has the same solutions as the inequality x -2. This also holds true in a less than andor equal sign and a greater than andor equal sign.

Solve the inequality dfrac 4x4 2 x 3 marks We need to get rid of the fraction first by multiplying by 2 4x4 2x Then subtract 4x 4 -2x Then divide by -2 -2 x Remember the sign changes direction when multiplying or dividing by a negative number. The inequality has the same solutions as the inequality. This is because in the inequality x 1 x is clearly greater than 1.

Thats because smaller negative numbers are closer to 0 making them worth more.

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