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

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

1. Isolate the term with \( x \): First, subtract \( \frac{5}{3} \) from both sides. \[ -2x = \frac{1}{6} - \frac{5}{3} \]

2. Find a common denominator: The common denominator between 6 and 3 is 6.

   • Convert \( \frac{5}{3} \) to sixths: \[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]
   • Now substitute back: \[ -2x = \frac{1}{6} - \frac{10}{6} = \frac{1 - 10}{6} = \frac{-9}{6} \]

3. Simplify: \[ -2x = \frac{-3}{2} \]

4. Solve for \( x \): Divide both sides by -2. \[ x = \frac{-3/2}{-2} = \frac{-3}{2} \times \frac{-1}{2} = \frac{3}{4} \]

The solution is: \[ \frac{3}{4} \]

Thus, the answer is \( \frac{3}{4} \).

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

−3.06
−
3.06
negative 3.06

−30.6
−
30.6
negative 30.6

−1.224
−
1.224
negative 1.224

−52.1

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

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

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

3. Divide both sides by 0.2 to get \( x \): \[ x = \frac{-6.12}{0.2} \]

4. Calculate the division: \[ x = -6.12 \div 0.2 = -30.6 \]

Therefore, the solution to the equation \( 0.2x - 2.15 = -8.27 \) is: \[ -30.6 \]

So the answer is \( -30.6 \).