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If you multiply or divide both sides of an inequality by a number you need to reverse the inequality sign?
negative flip
Why do you flip the inequality sign when dividing by a negative?
When you divide or multiply both sides of an inequality by a negative number, the order of the values changes, which can reverse the relationship between them. For example, if ( a < b ) and you multiply both sides by -1, the inequality becomes ( -a > -b ). This flip is necessary to maintain the truth of the statement, ensuring that the inequality reflects the correct relationship after the operation. Thus, it's a mathematical rule that helps preserve the validity of the inequality.
Why do we flip the inequality symbol when multiplying or dividing by a negative number.?
We flip the inequality symbol when multiplying or dividing by a negative number because it preserves the logical relationship between the quantities involved. For example, if ( a < b ) and we multiply both sides by a negative number, the direction of their relationship changes; thus, ( -a > -b ). This is due to the nature of the number line, where multiplying or dividing by a negative number reverses the order of the numbers. Therefore, flipping the symbol ensures that the inequality remains true.
How do you solve inequality and graph them?
Get the variables on one side of the inequality sign, and the numbers on the other side. You do this by using inverse operations. Divide the number by the variable. If you divide using a negative number you flip the inequality sign. An example of what you are looking at should look like x > 3. You would graph this example by drawing a number line, then putting an open cirlce at three, and shading the number line on the right side of the three. This shows that x is greater than three.
Do the same rules apply when you solve equations and inequalities?
Almost. There's one new rule, which is that whenever you multiply or divide by a negative number, you have to flip the inequality sign. To see why, try achieving the same result without this step, using positive factors and subtraction: the equation must effectively flip itself around the sign.
If you multiply or divide both sides of an inequality by a number you need to reverse the inequality sign?
negative flip
When you divide both sides of any inequality by a negative number you need to what the inequality symbol?
Flip it around
When is the only time you flip an inequality sign?
When you divide both sides of an inequality by a negative number, the inequality sign flips.
Do you flip the sign of this inequality 8x plus 4y12?
Only when you multiply or divide by a negative number
Do you flip the inequality sign if the only the variable is negative?
No, you only flip the inequality sign if you are dividing by a negative number on both sides of the inequality
Do you flip the inequality when adding and subtracting?
No. Only flip the inequality when multiplying or dividing by a negative number.
When do you have to flip the greater than or less than or equal to sign in a inequality equation?
You need to flip the inequality sign when you multiply or divide both sides of the inequality by a negative number. For example, if you have an inequality like ( -2x < 6 ) and you divide by -2, it becomes ( x > -3 ). However, when adding or subtracting a number from both sides, the inequality sign remains unchanged.
When you divide both sides of an inequality by a negative number you need to blank the inequality symbol?
Flip. You need to reverse the inequality when multiplying or dividing by a negative. -2x < 10 (-1)*(-2x) < (-1)*10 2x > -10 x > -5
Why must you flip the inequality symbol when you divide by a negative number?
For the same reason you must flip it when you multiply by a negative number. An example should suffice. 2 < 3 If you multiply by -1, without switching the sign, you get: -2 < -3, which is wrong. Actually, -2 > -3. Look at a number line if you are not sure about this - numbers to the left are less than numbers further to the right. Dividing by a negative number is the same as multiplying by the reciprocal, which in this case is also negative. These signs are strictly the "Greater than" and "Less than" signs. The inequality sign is an = with a / stroke through it. If you divide an inequality by -1 it remains an inequality.
Why do you flip the inequality sign when dividing by a negative?
When you divide or multiply both sides of an inequality by a negative number, the order of the values changes, which can reverse the relationship between them. For example, if ( a < b ) and you multiply both sides by -1, the inequality becomes ( -a > -b ). This flip is necessary to maintain the truth of the statement, ensuring that the inequality reflects the correct relationship after the operation. Thus, it's a mathematical rule that helps preserve the validity of the inequality.
What must you do when solving an inequality with a negative coefficient?
Divide by negative one and flip the sign eg -x > 6 / -1 /-1 x < - 6
How do you solve an inequality with a negative coefficient?
The easiest way is to "flip" the inequality symbol end divide by the negative number:Example:6 < 3 - 3s6 - 3 < 3 - 3s -33 < -3s Method a) Divide by negative coefficient and flip the inequality symbol3/-3 > -3s/-3-1 > s or s< -13 < -3s Method b) Full algorithm, eliminate -3s by adding 3s on both sides3 +3s < -3s + 3s3 + 3s < 03 - 3 + 3s < 0 -33s < -33s/3 < -3/3s < -1 Looks familiar? So basically if you perform the full algorithm (method b) you can understand why we flip the inequality symbol when we have to eliminate a negative coefficient but it is faster just to flip the symbol (method a)
