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Yes, but with the following two rules to remember. If you multiply or divide both sides by a negative number, then the inequality sign is reversed (> becomes <, or < becomes >). Adding and subtracting numbers have no effect on the direction of the inequality. Also, if you have a 'not equals' sign, then it is unaffected by the multiplication.
The same is true if you take the reciprocal of both sides.
Example: with the equation: 1/x = 2, take the reciprocal and x = 1/2. With the inequality 1/x < 2, this becomes x > 1/2. You could also solve it by multiplying both sides by x, then dividing both sides by 2, and get 2 < x, which is the same as x > 2.
Another example: 3 - x > 7. Subtract 3 from both sides: -x > 4. Multiply both sides by -1: x < -4.
You could also go about this as: add x to both sides: 3 > 7 + x, then subtract 7 from both sides: -4 > x, which means the same as x < -4
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Why can linear equations and linear inequalities be solved the same way?
Somewhat, but the rules are a bit different for inequalities. Example. -2X > 4 X < - 2 See, sign changes when dividing by negative coefficient.
How do you solve algebra inequalities?
Algebraic inequalities can be solved in the same fashion as algebraic equations. The goal here, as in algebraic equations, is to isolate the variable. The one thing to remember, however, is that when dividing or multiplying both sides by a negative number, one must switch the inequality sign.
Are the methods for solving linear and compound inequalities the same?
Yes
Can a linear equation and a linear Equality be solved the same way?
Yes.
What are linear equations with the same solutions called?
They are called simultaneous equations.
