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Algebraic Expression

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Variables A variable is a symbol that is used to represent an unknown quantity. For example, x, y, z. If x and y are variables, then the product xy is also a variable. Terms A term can be: a single number. For example, 2, 5. a variable, or a product of variables (which may be raised to powers). For example, z, b3, [pic]. a product of a number and one or more variables (which may be raised to powers). For example, 3x, – 4yz, 7a2 b3 . Coefficients In a term that is the product of a number and one or more variables, the number is called the numerical coefficient or simply the coefficient. For example, in the term –2b3, the coefficient is –2 and the variable part is b3. Like and unlike algebraic terms Like algebraic terms …show more content…

A linear equation has only one unknown quantity and therefore can have only one solution or root. This is the value of the unknown quantity that satisfies the equation. Solving a linear equation means finding its root. The most basic method of solving an equation involves the properties of equality. Properties of equality The solution of an equation does not change if we (i) add the same quantity to both sides of the equation. i.e. if a = b, then a + c = b + c. (ii) subtract the same quantity from both sides of the equation. i.e. if a = b, then a – c = b – c. (iii) multiply both sides of the equation by the same non-zero quantity. i.e. if a = b, then ac = bc. (iv) divide both sides of the equation by the same non-zero quantity. i.e. if a = b, then [pic]. In short, whatever is done to one side must be done to the other side. Strategy for solving linear equations 1. Eliminate any fractions by multiplying each side by the LCD. 2. Use the distributive property to remove brackets. 3. Combine any like terms. 4. Use the addition and subtraction properties of equality to get all variables on one side and numbers on the other side. 5. Use the multiplication and division properties of equality to get a single variable on one side. 6. Check by substituting your solution in the original equation. Ex. Solve the following equations: (1) x + 8 = 1 (2) y – 3 = –4 (3) 5b = 15 (4) [pic]

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