How do you solve for r in #4(r+3)=t#?

2 Answers
Mar 17, 2016

Answer:

r=t-12/4

Explanation:

4[r+3]=t
4r+12=t
4r=t-12
r=t-12/4

Mar 17, 2016

Answer:

#color(green)(" "r=t-3)#

Explanation:

Why the shortcut method works:

#color(blue)("Explaining from first principles about multiplying out a bracket")#

Consider the following:
#2a" is the same as "a+a#
#3a" is the same as "a+a+a#
#4a" is the same as "a+a+a+a#

So it follows that

#4(r+3)" is the same as " (r+3)+(r+3)+(r+3)+(r+3)#

From this you can see that there is 4 lots of r and 4 lots of 3's

So when multiplying out the bracket we have the equivalent of

#color(brown)(4color(blue)((r+3))" "->" "(4color(blue)(xxr))color(blue)(+)(4color(blue)(xx3))#

So #4(r+3) = 4r+12#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Solving your question")#

Given:#" "4(r+3)=t#

This is the same as:

#" "color(brown)(4r+12=t)#

We are told that we need to solve for r. That means we must end up with only one r in the equation and that it is to be on the left hand side of the equals sign. Everything else is to be on the other side.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Step 1")#

Collect all the terms with r on the left of = and everything else on the right. So we need to move the 12 to the other side.

To remove 12 from the left we do the following

Subtract #color(blue)(12)# from both sides

#" "color(brown)(4r+12color(blue)( -12)=tcolor(blue)(-12))#

But #+12-12=0#

#" "4r+0=t-12#

#" "4r=t-12#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Step 2")#

Any number multiplied by 1 does not change its value. We need r on its own. So we change the 4 into 1

Divide both sides by #color(blue)(4)#

#" "(4r)/4=t/4-12/4#

This is the same as

#" "4/4xxr=t/4-12/4#

But #4/4 = 1 # giving

#" "1xxr=t-12/4#

#" "r=t/4-12/4#

But #-12/4 = -3#

#" "r=t/4-3#

'///////////////////////////////////////////////////////////////////////
#color(blue)("The short cut rules that achieve the same thing are:")#

#color(brown)("To move something to the other side of the equals.")#

For add, move the term to the other side of the = and change the sign to subtract.

For subtract, move the term to the other side of the = and change the sign to add.

For multiply, move the term to the other side and divide by it.

For divide, move the term to the other side of the = and multiply by it.

Hope this helps in solving other question.