2. Solve for x and check.

 

(2/3)x+5/6=(1/4)x+3/8

This is an equation which has fractions. It will make things

easier if we clear denominators first. Multiply both sides by the

smallest common denominator, which, in lthis case, is 24.

 

 

24((2/3)x+5/6)=24((1/4)x+3/8)

 

To multiply a side of an equation by something, put

parentheses around the side of the equation and put the thing you

are going to multiply it by in front of the parentheses. The

parentheses indicate that we had the expression inside the

parentheses together before we decided to multiply it by something.

However, we now what to do with the parentheses. Multiply the

factor outside the parentheses by all of the terms inside.

 

 

24((2/3)x)+24(5/6)=24((1/4)x)+24(3/8)

 

 

When we simplify,

 

24((2/3)x)+24(5/6)=24((1/4)x)+24(3/8)

 

all of the denominators will be cleared out. That is because a

common denominator is something that all denominators go into.

 

Multiply the surviving factors

 

16x+20=6x+9

 

Transpose.

 

 

16x-6x=-20+9

Combine

 

10x = -11

 

Divide both sides by the coefficient of the unknown.

 

x=-11/10

 

Check

Copy down the original equation

 

(2/3)x+5/6=(1/4)x+3/8

 

except that instead of copying down the unknown, copy down the

solution in parentheses.

 

(2/3)(-11/10)+5/6=(1/4)(-11/10)+3/8.

 

 

In this order of operations problem do the multiplication of

fraction first.

 

-22/30+5/6=-11/40+3/8

 

The 22/30 will reduce, but we would have to reverse the

process when we find common denominators. Since we are adding

fractions, we need common denominators.The smallest common

denominator on the left side is 30, and the smallest common

denominator on the right hand side is 40.

 

-22/30+(5/6)(5/5)=-11/40+(3/8)(5/5)

 

or

 

-22/30+25/30=-11/40+15/40

 

which combine to

 

3/30=4/40

 

which simplifies to

 

1/10=1/10

 

and the solution checks.

 

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