Algebra Solving equations. Review Solve the following: 3+ -5-4 - -6 Evaluate the expression when x = 3 3x + 2 Simplify the expression: 3x + 5y - 2x +

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Presentation transcript:

Algebra Solving equations

Review Solve the following: Evaluate the expression when x = 3 3x + 2 Simplify the expression: 3x + 5y - 2x + y

Algebraic equations An equation is a mathematical statement that shows two quantities are equal. When the equation contains a variable, we use algebra to find the value of the variable

Example Solve the equation2x - 1 = 9 When x equals 52(5) - 1= 9 the statement is true = 9 9 = 9

Solving equations Think of the equation as a balance. What you do to one side, you must do to the other side. Basic strategy: isolate the variable How? Use inverse operations Addition and subtraction are inverse operations Multiplication and division are inverse

Practice Solve the following equation: x - 13 = 25 Isolate the variable add (inverse of subtraction) 13 to both sides

More practice Solve: 1) 5x = -35 2) x + 40 = 75 3) x/2 = 5 Check your answer by plugging it back in!

Solving multi-step equations Some equations involve more than one operation. Reverse the order of operations 5x - 10 = 35

Practice 6x + 7 = 374x + 5 = 21

Variables on both sides When there are variables on both sides, move them to one side Guide: Move the smaller amount 12x + 9 = 10x + 1

Practice 3x - 8 = x + 48x + 12 = x

Parentheses Remove the parentheses by distributing the factor 3(x + 1) = -12

Practice 5(x + 1) = 755(x - 7) = 5

Word problems During lunch one day, a cafe sold 8 more turkey sandwiches than ham sandwiches. If there were 32 sandwiches sold in all, how many were ham sandwiches? Assign the variable

Another word problem Rae’s weekly income is $250 less than twice her husband’s. Together they earn $890 per week. Write an equation that can be used to find her husband's weekly earnings.