Algebra Basics

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What is a variable in algebra?
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A symbol, often a letter, used to represent an unknown number in mathematical expressions or equations.
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What is the purpose of an algebraic equation?
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To represent a relationship between variables and constants that can be solved to find the value of the variables.
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What does the term 'like terms' mean?
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Terms in an algebraic expression that have the same variables raised to the same power.
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What is the distributive property?
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A property stating that a(b + c) = ab + ac, used for expanding expressions.
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What is a coefficient?
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A numerical or constant quantity placed before a variable in a term.
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Describe a linear equation.
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An equation that makes a straight line when graphed and has no variables raised to a power higher than one.
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How do you solve a simple linear equation like 2x + 3 = 7?
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Subtract 3 from both sides to get 2x = 4, then divide both sides by 2 to find x = 2.
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What is an inequality?
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A mathematical statement comparing two expressions, typically using <, >, ≤, or ≥ signs.
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What is meant by 'solving for a variable'?
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Determining the value of the variable that makes an equation or inequality true.
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What is a quadratic equation?
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An equation where the highest exponent of the variable is 2, usually in the form ax^2 + bx + c = 0.
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How do you simplify an expression like 3x + 5x?
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Combine like terms to get 8x.
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Explain the zero-product property.
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If the product of two factors is zero, at least one of the factors must be zero.
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How can you check the solution of an equation?
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Substitute the solution back into the original equation and verify that both sides are equal.
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What does the term 'factor' mean in algebra?
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To express a number or expression as a product of its divisors or terms.
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What is an exponent in algebra?
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A number that indicates how many times a base is multiplied by itself.
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