Let’s solve the equation step by step. The given equation is:

$\frac{2}{3} = -\frac{1}{2}x + \frac{2}{7}$

Step 1: Eliminate the fractions by finding a common denominator

The denominators are 3, 2, and 7. The least common denominator (LCD) is $42$. Multiply through by $42$ to eliminate all fractions:

$42 \cdot \frac{2}{3} = 42 \cdot \left(-\frac{1}{2}x\right) + 42 \cdot \frac{2}{7}$

Simplify each term:

• $42 \cdot \frac{2}{3} = 28$
• $42 \cdot \left(-\frac{1}{2}x\right) = -21x$
• $42 \cdot \frac{2}{7} = 12$

The equation becomes: $28 = -21x + 12$

Step 2: Isolate the variable term

Subtract $12$ from both sides: $28 - 12 = -21x$ $16 = -21x$

Step 3: Solve for $x$

Divide both sides by $-21$: $x = \frac{16}{-21}$

Simplify: $x = -\frac{16}{21}$

Final Answer:

$x = -\frac{16}{21}$

Let me know if you have any questions or need further clarification!

Related Questions:

1. How do you find the least common denominator of fractions?
2. Why is it important to eliminate fractions in equations?
3. Can this problem be solved using decimals instead of fractions?
4. What are the steps to check your solution in such equations?
5. How do you simplify improper fractions?

Tip: When working with fractional coefficients, always verify the LCD to avoid mistakes in calculations.