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

                $\div2\div2\div2$

                 $y=\frac{6-5x}{2}$