These things do not affect the direction of the inequality:

A radical equation is one where the variable appears under a square root sign. (For the time being we only worry about square roots, not cube roots or other interesting things.) The general technique for solving a radical equation is: isolate the square root sign (and whatever’s under it) on one side of the equation.

A radical inequality is an inequality that contains a variable within a radical. You can solve radical inequalities by graphing or using algebra. A radical expression with an even index and a negative radicand has no real roots. Remember!

1. Add (or subtract) a number from both sides.
2. Multiply (or divide) both sides by a positive number.
3. Simplify a side.

The function y = x2 is increasing for x ≥ 0. (Figure 1) Hence squaring both sides of an inequality will be valid as long as both sides are non-negative. Since square roots are non-negative, inequality (2) is only meaningful if both sides are non-negative. Hence, squaring both sides was indeed valid.

Taking a square root will not change the inequality (but only when both a and b are greater than or equal to zero).

There are five systems or types of social inequality: wealth inequality, treatment and responsibility inequality, political inequality, life inequality, and membership inequality. Political inequality is the difference brought about by the ability to access governmental resources which therefore have no civic equality.

Taking the reciprocal of both a and b can change the direction of the inequality. The general rule is that when a < b then: If (1/a ) > (1/b) when a and b are positive. That is, flip the inequality.

The main situation where you’ll need to flip the inequality sign is when you multiply or divide both sides of an inequality by a negative number. To solve, you need to get all the x-es on the same side of the inequality. Subtract 6_x_ from both sides in order to only have x on the left.

The reciprocal or multiplicative inverse of a number x is the number which, when multiplied by x , gives 1 . So, the product of a number and its reciprocal is 1 . (This is sometimes called the property of reciprocals .)

To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

The reciprocal of 2 is 1/2. The reciprocal of a number can be found when 1 is divided by the number you wish to find the reciprocal of.

A number’s reciprocal is the upside down version of that number when it’s written as a fraction. Another name for reciprocal is multiplicative inverse. Reciprocals are really helpful when it comes to dividing fractions. We can use reciprocals to turn fraction division into fraction multiplication.

More Examples:

Reciprocal of 9/10 is 10/9.

To find the reciprocal you switch the numerator and denominator, so the reciprocal is 12/11.

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