What is the solution of the equation 5/3−2x=1/6 ?(1 point)

Question

Responses

3
3

−11/12
negative Start Fraction 11 over 12 End Fraction

3/4
Start Fraction 3 over 4 End Fraction

−11/3

Answer 1

To solve the equation \( \frac{5}{3} - 2x = \frac{1}{6} \), we can follow these steps:

1. Isolate the term with \( x \): \[ -2x = \frac{1}{6} - \frac{5}{3} \]

2. Find a common denominator to subtract the fractions. The least common multiple of 6 and 3 is 6. We can express \( \frac{5}{3} \) with a denominator of 6: \[ \frac{5}{3} = \frac{10}{6} \]

3. Now substitute this back into the equation: \[ -2x = \frac{1}{6} - \frac{10}{6} \] \[ -2x = \frac{1 - 10}{6} = \frac{-9}{6} \] \[ -2x = -\frac{3}{2} \]

4. Divide both sides by -2: \[ x = \frac{-\frac{3}{2}}{-2} = \frac{3}{4} \]

Thus, the solution to the equation \( \frac{5}{3} - 2x = \frac{1}{6} \) is: \[ \boxed{\frac{3}{4}} \]

So the correct response is \( \frac{3}{4} \) (Start Fraction 3 over 4 End Fraction).

Answer 2

What is the solution of the equation 0.2x−2.15=−8.27?(1 point)
Responses

−52.1
negative 52.1

−3.06
negative 3.06

−30.6
negative 30.6

−1.224

Answer 3

To solve the equation \( 0.2x - 2.15 = -8.27 \), follow these steps:

1. Add 2.15 to both sides of the equation: \[ 0.2x = -8.27 + 2.15 \]

2. Calculate the right side: \[ -8.27 + 2.15 = -6.12 \] So, we have: \[ 0.2x = -6.12 \]

3. Now, divide both sides by 0.2 to solve for \( x \): \[ x = \frac{-6.12}{0.2} \]

4. Calculate \( \frac{-6.12}{0.2} \): \[ x = -30.6 \]

Thus, the solution to the equation \( 0.2x - 2.15 = -8.27 \) is: \[ \boxed{-30.6} \]

So the correct response is \( -30.6 \) (negative 30.6).