4(x-1/2)-6(x-1/3)=1/3(15-x)

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

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4 ( x - 1/2) - 6 ( x - 1/3) = (1/3) ( 15 - x)

First we will expand brackets:

==> 4*x + 4*-1/2  - 6*x - 6*-1/3 = (1/3)* 15 + (1/3)*-x

==> 4x  - 2 - 6x + 2 = 5 - (1/3)x

Now we will combine like terms:

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

==> -2x = 5 - (1/3) x

Now let us multiply by 3:

==> -6x = 15 - x

Add 6x to both sides:

==> 0 = 15 - x + 6x

==> 0 = 15 + 5x

Now subtract 15 from both sides:

==> -15 = 5x

Divide by 5:

==> -3 = x

Then the answer is: x = -3

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cdepp | Elementary School Teacher | (Level 1) eNoter

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4(x-1/2)-6(x-1/3)=1/3(15-x)

This is a first-degree (linear) equation with one variable.

To solve for x:

Expand the parethetical expressions

4x-2-6x+2=5-x/3

Multiply both sides by 3 to eliminate the fraction

12x-6-18x+6=15-x

Add x to both sides of the equation

13x-6-18x+6=15

Combine like terms

-5x=15

Divide both sides of the equation by -5

x=-3

CHECK by substituting all x's with -3 and solve

4(x-1/2)-6(x-1/3)=1/3(15-x)

4(-3-1/2)-6(-3-1/3)=1/3(15-(-3))

-12-2+18+2=1/3(18)

6=6

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve the equation, 4(x-1/2)-6(x-1/3)=1/3(15-x):

This is a linear equation in one variable. We open the paranthis and bring all like  x's to one side.

4x-4(1/2) - 6x-6(-1/3) =(1/3)15-x/3.

4x-2 -6x +2 = 5 - x/3.

4x-6x   5-x/3 

-2x = 5-x/3.

We add x/3 to both sides:

-2x+x/3 = 5.

-5x/3 = 5.

We multiply by 3 both sides:

-5x = 5*3 = 15.

We divide both sides by -5:

x = 15/-5 = -3.

Therefore x = -3.

Tally: Put x= -3 inthe given equation  4(x-1/2)-6(x-1/3)=1/3(15-x)

LHS: 4(-3-1/2)-6(-3-1/2) = 4*(-3.5)-6(-3-1/3) = -14+20 = 6

RHS =(1/3)(15-x) = (1/3)(15-(-3)) = (1/5)(18) = 6.

 

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