Solving Algebraic Equations. Equality 3 = 3 3+4 = 3+4 3+4 = 7 For what value of x is: x + 4 = 7 true?

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Presentation transcript:

Solving Algebraic Equations

Equality 3 = = = 7 For what value of x is: x + 4 = 7 true?

Equality 3 = = = 7 For what value of x is: x + 4 = 7 true? Answer: when x=3, then the equation is true.

How do I Solve Algebraic Equations? 1.What ever you add, subtract, multiply or divide to one side of the equation, you have to do the same to the other side of the equation! 2.Try to isolate the variable to one side of the equation. 3.Always substitute your answer for the variable to see if the answer and equation are true!

Example #1: x+4=7 x+4+(-4) = 7 + (-4) x + 0 = 3 x = 3 Substituting: = 7 7 = 7 (CHECK!)

Example #2: 2x=4 2∙x 4 1∙x = 2 x = = Substituting: 2x= 4 2∙2= 4 4 = 4 (CHECK!)

PROBLEMS: Solving Algebraic Equations Are you ready… 3,2,1… here we go!

Solve the Equation: v – 10 = -9

Answer: v = v + 0 = 1 v = 1

Solve the Equation: v – 10 = -3

Answer: v – = v + 0 = 7 v = 7

Solve the Equation: x – 3 = 4

Answer: x – 3 +3 = 4 +3 x + 0 = 7 x = 7

Note: x – 3 = 4 X = X = 7

Getting back to Solving Equations… 3,2,1… here we go!

Solve the Equation: ― = 2 x5x5

Answer: (5)∙― = (5)∙2 1 ∙ x = 5∙2 x = 5∙2 (What do you notice?) x = 10 x5x5

Solve the Equation: 22 = -11k

Answer: = -2 = 1k -2 = k k = k -11

Solve the Equation: -13m = -377

Answer: m = 29

Solve the Equation: p + 8 = 14.1

Answer: p = 6.1

Solve the Equation: n = -4.7

Answer: n = -9.4

Solve the Equation: n = 0.7

Answer: n = -3.2

Solve the Equation: ― = -7 x 1.2

Answer: x = -8.4

Solve the Equation: -6.3k = -8.19

Answer: k = 1.3

Solve the Equation: 5½ + p = 6

Answer: p = ½

Solve the Equation: x – 3 = -5½

Answer: x = -2½

Solve the Equation: 9 ⅓ = ⁵⁄₃ ∙n

Answer: n = 5⅗

Solve the Equation: ―n = -1―

Answer: n = -1²⁄₉

Multiple Step Algebraic Equations

Solve the Equation: 1 – r = -5

Answer: r = 6

Solve the Equation: 3p – 2 = -29

Answer: p = -9

Solve the Equation: 4n - 9 = -9

Answer: n = 0

Solve the Equation: -5x + 13 = -17

Answer: x = 6

Solve the Equation: ― + 4 = 5 r 10

Answer: r = 10

Solve the Equation: ― + 5 = 3 n2n2

Answer: n = -4

Solve the Equation: = -7 k-10 2

Answer: k = -4

Solve the Equation: = 2 9+m 3

Answer: m = -3

Solve the Equation: = x 22

Answer: x = -17

Solve the Equation: -5 + ― = 0 n3n3

Answer: n = 15

Solve the Equation: ― + 8 = 7 p4p4

Answer: p = -4

Solve the Equation: ― - 5 = -8 y -4

Answer: y = 12

Solve the Equation: 0.4x = 5.78

Answer: x = 4.7

Solve the Equation: 9.2r =

Answer: r = 16.6

Solve the Equation: ― = m 2.8

Answer: m =

Solve the Equation: + = X2X

Answer: x = ⅖

Solve the Equation: x + 1 =

Answer: x = ⁸⁄₉