transforming formulas

transforming formulas

Transforming formulas

we are solving the formula for a different variable then it is solved for.

when solving y=15x + 2 we follow the steps for solving a two step equation

• we isolate the variable by removing the constant (+2) by subtracting 2

• y-2 = 15x + 2 - 2

• which leaves us with y - 2= 15x

• next step we isolate by dividing both sides by the coefficient (15)

•  $\frac{\left(y-2\right)}{15}=\frac{15x}{15}$  

•  $\frac{\left(y-2\right)}{15}=x$  

On equations that don't have a constant but have another term not attached to the variable you want to get ride of that term first.

•  $B=5T+2h$  

• let solve for T

Multiple Choice

What is my first step in Isolating the variable in the function B=5T+2h when solving for T?

• divide by 5

• divide by 2

• add b to both sides

• minus 2h to both sided

First step - 2h

•  $B-2h=5T+2h-2h$  

• This leaves us with  $B-2h=5T$  

Multiple Choice

what is our second step in solving for T?

• divide by 2

• divide by 5

• add b to both sides

• minus 2h to both sides

you divide both sides by 5

•  $\frac{\left(B-2h\right)}{5}=\frac{5T}{5}$  

•  $\frac{\left(B-2h\right)}{5}=T$  

Fill in the Blanks

 $\frac{\left(B-2h\right)}{5}=T\$   for the equation to the left what does T equal if B=24 and h=2

lets solve the equation

 $a=\frac{\left(4m+d\right)}{2}$   for d

• because of the parenthesis you have to get rid of the division of 2 by multiplying both sides by 2

•  $2a=\frac{\left(4m+d\right)2}{2}$  

•  $2a=4m+d$  

• now that we got rid of the parenthesis we can now isolate d

Multiple Choice

how do we isolate d in the equation 2a=4m+d

• divide by 2

• minus 4m to both sides

• minus 2a to both sides

• divide both sides by 4

minus 4m from both sides

•  $2a-4m=4m-4m+d$  

•  $2a-4m=d$  

Fill in the Blanks

what is d equal to in the equation
 $2a-4m=d$  if a=5 and m=7 

Multiple Select

now lets try one on your own. rewrite the equation

 $h=\frac{1}{2}vt$   for v

•  $\frac{ht}{2}=v$  

•  $\frac{h}{2t}=v$  

•  $\frac{2h}{t}=v$  

•  $\frac{h}{t}+\frac{1}{2}=v$  

 $\frac{2h}{t}=v$  

• In this formula you are dividing and multiplying and it doesn't matter which one you do first.

• divide both sides by t or multiply both sides by 2

•  $\frac{h}{t}=\frac{\left(\frac{1}{2}vt\right)}{t}\ or\ 2h=2\left(\frac{1}{2}vt\right)$  

• then do the step you didn't do from above next

•  $2\left(\frac{h}{t}\right)=2\left(\frac{1}{2}v\right)\ or\ \frac{2t}{t}=\frac{vt}{t}$  

Fill in the Blanks

solve for V when h=10 and t =-4

 $\frac{2h}{t}=v$