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The main difference is that when solving inequalities, if you multiply or divide by a negative number you have to be careful, since you then also have to switch the sign (for example, change a "less-than" sign to a "greater-than" sign). If you multiply or divide by an expression that contains a variable, you have to consider the two cases: that such an expression might be positive, or that it might be negative.
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What are the differences between real numbers and imaginary numbers?
The set of real numbers is not closed under powers. That is to say, there are some equations of the form y = xa which do not have a solution within the set. Typical example: x is negative, a = 0.5
Can some systems of inequalities have no solution?
true
What are the differences and similaries between expressions and equations?
An expression is any combination of symbols that can be evaluated to a number (or perhaps to some other data type). An equation has an equal sign, and an expression on both sides of the equal sign - it is a claim that the two expressions are equal.
What is the algebra vocabulary?
Algebra vocabulary refers to the terminology and symbols used in algebraic expressions, equations, and operations. Some common algebra vocabulary includes variables, constants, coefficients, exponents, terms, equations, inequalities, functions, and graphs. Understanding and using this vocabulary is essential for solving algebraic problems and communicating mathematical ideas effectively.
Do you have to use the same variables for all equations when creating a system of equations?
The idea is to work with the same variables, but it is possible that some of the variables are missing in some of the equations.
