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

Question

3/4
3
−11/3
−11/12

Answer 1

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

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

2. To subtract the fractions on the right side, we need a common denominator. The least common multiple of 6 and 3 is 6. Rewrite \( \frac{5}{3} \) with a denominator of 6: \[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]

3. Substitute back in: \[ -2x = \frac{1}{6} - \frac{10}{6} = \frac{1 - 10}{6} = -\frac{9}{6} = -\frac{3}{2} \]

4. Now, multiply both sides by -1 to solve for \( 2x \): \[ 2x = \frac{3}{2} \]

5. Divide both sides by 2 to isolate \( x \): \[ x = \frac{3}{2} \div 2 = \frac{3}{2} \times \frac{1}{2} = \frac{3}{4} \]

Thus, the solution to the equation is: \[ \boxed{\frac{3}{4}} \]

Answer 2

What is the solution of the equation 0.2x−2.15=−8.27?
−52.1
−1.224
−30.6
−3.06

Answer 3

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

1. Add 2.15 to both sides to move the constant term on the left side to the right side: \[ 0.2x = -8.27 + 2.15 \]

2. Calculate the right side: \[ -8.27 + 2.15 = -6.12 \] So the equation becomes: \[ 0.2x = -6.12 \]

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

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

Thus, the solution to the equation is: \[ \boxed{-30.6} \]