1, both sides of the inequality are multiplied or divided by a negative number;

2. The reciprocal of the inequality with the same sign (that is, positive or negative) needs to be changed.

Both sides of inequality are multiplied or divided by a negative number;

For example:

5> 1 times a negative number-1 and becomes -5.

It is necessary to change the sign of the reciprocal of inequality with the same sign (i.e. the same positive or negative);

Example: 3; 1/8, this is because of the nature of the fraction. The larger the denominator, the smaller the fraction value.

Edited in July 2020-65438+June.

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When does inequality change its sign?

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When do you need to change symbols to solve inequalities?

Application of Basic Properties of Inequality 34

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When do you need to change symbols to solve inequalities?

Multiply or divide a negative number on both sides of inequality to change the direction of inequality. Example: 5 & gt-3, both sides are multiplied by -2, and the result is-10.

Generally, pure greater than signs ">" and "less than signs", ≥, ≤, ≦) are called inequalities. Among them, the common area of analytical expressions on both sides is called inequality area. Algebraic expression inequality: both sides of algebraic expression inequality are algebraic expressions (that is, the unknown is not in the denominator). One-dimensional linear inequality: an unknown (that is, one dimension) and the degree of the unknown is 1 (that is, once). For example, 3-X >0 is the same: binary linear inequality: an inequality that contains two unknowns (namely binary) and the number of unknowns is 1 time (namely once).

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When to change the sign when solving inequality?

When the left and right sides of inequality are divided or multiplied by negative numbers at the same time, the sign of inequality needs to be changed. Take 2x-5 < 4x-2 as an example, the steps are as follows: Step 1: Add 5 to the left and right sides of the formula. As shown in the figure: Step 2: Calculate the constant and eliminate the constant on the left. As shown in the figure: Step 3: Move the formula to the left by 4x, so as to merge similar items (note: whether it is a constant or an unknown, whether it changes from left to right or right to left, the numerical value must be multiplied by-1, that is, the sign must be changed). As shown in the figure: Step 4: Merge similar items. Calculate 2x-4x and the result is -2x. As shown in the figure: Step 5: Divide the left and right sides of the formula by -2 to eliminate the coefficient on the unknown (the sign of inequality needs to be changed from the original ""due to division or multiplication of negative numbers). The final conclusion is: x >- 1.5, as shown in the figure:

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In the calculation of inequality, it is necessary to change the sign, add, subtract, multiply or divide negative numbers.

Both sides of the inequality add and subtract the same negative number at the same time, and the inequality does not need to be changed. Both sides of the inequality add and subtract the same real number at the same time. No matter whether the real number is 0, positive or negative, the sign of the inequality remains unchanged. I think this should be easy to understand. For example, if A > B holds, then a+(-3) and b+(-3) certainly hold. A+(-3) < B+(-3) cannot be established. This is not common sense. Both sides of the inequality multiply and divide a negative number at the same time, and the sign of the inequality should be changed. For example, if a > b holds, then both sides are multiplied by -2 to get -2a and -2b, and then -2a.

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When does inequality change its sign?

If the left side of the inequality sign is negative, then the inequality sign changes direction; If both sides of the unequal sign are negative, the unequal sign changes direction; The rest of the situation will not change direction.

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