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...
(anything to the power of 0 is 1)
(You subtract the powers: 0 - 3 = -3)