How do you solve #-4g = -20#?

For this equation, the variable is being multiplied by #-4#. In order to get the variable, #g#, by itself, we have to do the inverse operation of the operation that is being applied to the variable right now.

In this case, the variable is being multiplied, so the inverse operation of multiplication is division. Now, you have to divide the left side by #-4#. Now, whatever you do to one side, you have to do the same to the other. So, divide the right side by #-4#, and you will get your answer, #5#.

#color(red)("Some very important facts that will help with your maths")#

#color(blue)("Fact 1")#

First and foremost, an equation has to 'balance'. This means that the overall value of the left hand side must be the same as that of the right hand side.

Example: 2 = 2 is true; 2 = 3 is not balanced so is false

#color(blue)("Fact 2")#

For addition or subtraction: what you wish to move to the other side of the = you change to 0

Example: 6 = 6 #-> color(brown)(2+4 = 6)#

Subtract 2 from both sides #-> color(brown)(2color(blue)(-2)+4" " =" " 6color(blue)(-2))#

#0+4" "=" "4#

#color(blue)("Fact 3")#

For multiply or divide: what you do to move to the other side of = you change it to 1. As demonstrated in the solution to this question.
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#color(blue)("Answering your question")#

Given:#" "-4g=-20#

Multiply both sides by (-1) this changes the signs

#color(brown)(+4g=+20)#

Moving the 4 to the other side: divide both sides by #color(blue)(4)#

#color(brown)(4/(color(blue)(4))xxg=20/(color(blue)(4))#

But #4/4 = 1# and #1xxg=g#

#g=20/4#

Cancelling out the 4

#g=cancel(20)^5/cancel(4)^1#

#g=5#