Solving for variables

Solving equations

Solving simple equations

  • Sometimes in equation we aren’t given a number in a equation such as x

            Ex: 6x=12

  • To solve it we must isolate the variable on one side of the equation.

    • Inverse operations (we would use this on both sides of the equation by doing the inverse or opposite on both sides of the equation)

            Ex": 6x=12                                Inverse operations

                   \div6   \div6                                 write it

                    x=2 

Solving multistep equations   

  • Similar to simple equation

    • repeat inverse as many times needed

            Ex: 3\left(m-6\right)=-12                 distribute

                  3m-18=-12                   Inverse operations

                          +18    +18 

                  3m=6                                 Inverse operations

                    m=2 

Solving equations (variable on both sides)

  • Basically the same

  • combine like terms instead

    • if has same variable and exponent can combine(for-+ )

    • only the number changes

            Ex: 3x+3x=6x

  • combining like terms (for x \div )

    • variable and exponent doesn’t matter (only now for exponents the coefficient must stay the same)

    • exponent if multiply add, if divide subtract

    • variable stack

            Ex: 3x\cdot4m=12xm                 

                  6^2\cdot6^3=6^5

  • Solve

            Ex:6y+5=2y-3                    Inverse operations

              -2y -5-2y -5                    combine terms

                 4y=-8                                   Inverse operations

                  y=-2

Rewriting Equations

  • Literal equation: an equation that has 2 or more variable

            Ex: e=mc^2

  • you will solve for a specific variable

    • same thing isolate the variable

(solve for y)

            Ex:2y+5x=6                             Inverse Operations

                  -5x -5x

                 2y=6-5x                             Inverse

                \div2\div2\div2

                 y=\frac{6-5x}{2}