How do you solve #1/8x-5=3#?

1 Answer
Oct 30, 2015

Answer:

#x=64# See detailed explanation for how you do it!

Explanation:

#color(red)("Change things so that there is only one")# #color(red)(x)# #color(red)("and it is on the left of the = sign. Everything else is to be on the right of the = sign")#

Brackets use only to show what parts are being changed. The brackets are only for demonstration to you what is happening. They serve no other purpose.

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Step1
Move the 5 from left to right

#color(brown)("In add or subtract, if we can change a number to zero"# #color(Brown)("it has no effect. This is the same as removing it from that side of the equation.")#

Add 5 to both sides giving
#(1/8x-5) +5 = (3) +5#

#1/8x +0 =8# ................................(1)

I have used plus 5 because negative 5 and plus 5 make zero.
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Step 2

Rewrite equation (1) as:

#1/8x = 8# ...............................(2)

#color(brown)("In this case if we can change the")# #color(brown)(1/8)##color(brown)("into 1 we are then multiplying")# #color(brown)(x)# #color(brown)("by 1. Consequently not changing its value")#

Multiply both sides of equation (2) by 8

#(1/8 x) times 8= (8) times 8#

But #1/8 times 8# is the same as #8/8# which is 1 so now we have changed equation (2) to

#1 times x = 64#
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There you have it: Only #x# on one side and its value on the other.