Math 017 Materials With Exercises

Lesson 8__________________________________________________________________________________Topics: Generalities on equations; Solving linear equations in one unknown.__________________________________________________________________________________This lesson introduces an important algebraic concept: equations.EquationsEquationA mathematical statement consisting of two expressionsseparated by an equal sign is called an equation.The following are examples of equations.2 3 5, 3x 5, x 3 y .We will refer to expressions on the left of the equal sign as the left-hand side of the equation and tothe expressions on the right of the equal sign as the right-hand side of the equation. In x 3 y ,x 3 is the left-hand side of the equation, and y is the right-hand side of the equation. We canalways reverse sides of the equation. For instance, instead of x 3 y , we can write y x 3. Bothstatements have exactly the same meaning.The difference between equations and algebraic expressionsNotice the difference between an equation and algebraic expression. Equations are two algebraicexpressions separated by the equal sign. There is always the left-hand side and the right-hand side ofeach equation. Algebraic expressions are different from equations. For example, x y 3x 2 is anequation, but x y , 3x 2 are simply algebraic expressions.Example 8.1 Determine whether the following mathematical sentences represent an equation or analgebraic expression. Any time you find an equation, circle its left-hand side.a) 4x 2b) 4x 2 7c) x2 3y2 4 xSolution:Only b) and c) are equations. The left hand sides: 4x 2 7, x2 3y2 4 x77