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pogonyaev
3 years ago
6

Aljabra.

e="x \div 12 - 3x - 1 \div 8 = 1" alt="x \div 12 - 3x - 1 \div 8 = 1" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
laila [671]3 years ago
3 0

Answer: -27/70

Step-by-step explanation:

x ÷ 12 − 3x − 1 ÷ 8 = 1

Simplify x ÷ 12 − 3x − 1 ÷ 8.

  Rewrite the division as a fraction.

        x /12 − 3x − 1 ÷ 8 = 1

   Rewrite the division as a fraction.

        x/12− 3x − 1/8 = 1

  To write −3x as a fraction with a common denominator, multiply by  12/ 12

        x/12− 3x ⋅ 12/12 − 1/8 = 1

  Simplify terms.

   Combine −3x and  12/12

        x /12−3x ⋅ 12/12 − 1/8  = 1  

  Combine the numerators over the common denominator.

        (x − 3x ⋅ 12/12) − (1/8)  = 1

  Simplify the numerator.

        (x ⋅ −35/12) -(1/1) =  1

  Move −35 to the left of x.

        −(35 ⋅ x/12) -(1 /8) = 1

   Move the negative in front of the fraction.

        -(35x/12) −(1/8) = 1

Move all terms not containing x to the right side of the equation.

  Add 1/8 to both sides of the equation.

        -(35x/12) = 1 + (1/8)

  Write 1 as a fraction with a common denominator.

        -( 35x /12) =  8/8 + 1 /8

    Combine the numerators over the common denominator.

        -( 35x /12) =  8+1/8

  Add 8 and 1.

        -( 35x /12) =  9/8

Multiply both sides of the equation by − 12/35

        -( 12 /35) ⋅ (− 35x /12 ) = − 12/35 ⋅ 9/8

Simplify both sides of the equation.

   Simplify -( 12 /35) ⋅ (− 35x /12 )

   Cancel the common factor of 12.

              −1/35⋅ (−35x) = − 12/35 ⋅ 9/8

    Cancel the common factor of 35.

               −1 ⋅ (−x) = − 12/35 ⋅ 9/8

   Multiply −1 by −1.

                   1 ⋅ x = − 12/35 ⋅ 9/8

      Multiply x by 1.

                   x = − 12/35 ⋅ 9/8

   Simplify − 12 /35  ⋅ 9/8

   Cancel the common factor of 4.

                   x = −3/35 ⋅ 9 /2

   Multiply −3/35 and 9/2 .

                   x= (−3 ⋅ 9)/( 35 ⋅ 2 )

    Simplify the expression.

   Multiply −3 by 9.

                   x = -27/(35 ⋅ 2)

   Multiply 35 by 2.

                   x= -27/70

The result can be shown in multiple forms.

Exact Form:   x= -27/70

Decimal Form:  x  = −0.3857142...

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