Algebra 2 Miss Hudson’s Maths

To strip terms away - do the opposite! Solving Equations The aim is to find the value of the variable that makes the mathematical sentence true. To do this we need to step by step strip all other terms away from the variable (usually x) ie isolate the x What you do to one side, you do to the other in order to keep the sides balanced. x 7 = 3 eg 1: x 7 6x = 18 eg 3: x 7 6 6 x = 21 x = 3 + 4 + 4 eg 2: x - 4 = 7 To strip terms away - do the opposite! x = 11 Miss Hudson’s Maths

eg 5: (gives a negative answer) eg 6: (gives a fractional answer) + 5 + 5 eg 4: 2x - 5 = 3 2x = 8 2 2 x = 4 eg 5: (gives a negative answer) eg 6: (gives a fractional answer) -15 -15 -1 -1 6x + 1 = 9 2x + 15 = 1 2x = -14 6x = 8 2 2 6 6 4 or 1 1 3 x = -7 x = 3 Miss Hudson’s Maths

x eg 7: - 4 = - 3 3 x = 1 3 x = 3 2 x - 4 eg 8: = -2 3 2 x - 4 = -6 +4 +4 eg 7: - 4 = - 3 3 x 3 x x 3 = 1 3 x = 3 x 3 2 x - 4 x 3 eg 8: = -2 3 + 4 + 4 2 x - 4 = -6 2 x = - 2 2 2 x = - 1 Miss Hudson’s Maths

Equations with Brackets eg 9: 3 ( 2 y - 1 ) = 21 Expand the brackets first; so we go 3 x 2y and 3 x -1 = + 3 + 3 6 y - 3 = 21 6 y = 24 6 6 y = 4 Miss Hudson’s Maths

Collect the numbers on the other side If x appears on both sides of the equation we need to collect all the x’s on the side that has most of them first. -3x -3x eg 10: 5x = 3x + 8 2x = 8 2 2 Collect the numbers on the other side x = 4 + 4x + 4x eg 11: -4x + 8 = 2x - 20 + 20 + 20 8 = 6x - 20 28 = 6x 6 6 4⅔ = x Miss Hudson’s Maths

Writing Equations & Solving Them eg 1: I am thinking of a number. If I multiply this number by 3, I get a result of 18. What is the number? Solution: Let the number be x 3x = 18 3 3 x = 6 The number is 6 eg 2: When 4 times a number is added to 5 the result is 17. Find the original number by forming an equation and solving it. Solution: Let the number be n -5 -5 4n + 5 = 17 4n = 12 4 4 n = 3 The number is 3 Miss Hudson’s Maths

eg 3: Twice a certain number is 7 more than the number. What is the number? Solution: Let the number be x -x -x 2x = x + 7 x = 7 The number is 7 eg 4: When 3 times a number is added to the original number the result is 16. Find the original number by forming an equation and solving it. Solution: Let the number be n 3n + n = 16 4n = 16 4 4 n = 4 The number is 4 Miss Hudson’s Maths

Write an algebraic expression for each of the following statements Eight is added to the number n. Six is added to three times the number n. Four is added to five times a certain number x. Thirty is subtracted from six times a certain number y. A certain number m is multiplied by negative five and then eight is added. A certain number q is divided by four and then six is added. Twelve is divided by negative x. The number x is multiplied by negative three and the result is divided by five. Four times the number z is subtracted from negative three. Three times the number y is divided into negative twelve. Write an algebraic expression for each of the following statements Miss Hudson’s Maths