Answer: -27/70
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...