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Solve for 
x.

(3x-5)/(8)-(3x-9)/(40)=2
Answer:

Solve for x \mathrm{x} .\newline3x583x940=2 \frac{3 x-5}{8}-\frac{3 x-9}{40}=2 \newlineAnswer:

Full solution

Q. Solve for x \mathrm{x} .\newline3x583x940=2 \frac{3 x-5}{8}-\frac{3 x-9}{40}=2 \newlineAnswer:
  1. Find common denominator: Find a common denominator for the fractions.\newlineThe denominators are 88 and 4040. The least common denominator (LCD) for 88 and 4040 is 4040.
  2. Convert first fraction: Convert the first fraction to have the common denominator of 4040. To convert (3x5)/8(3x-5)/8 to a fraction with a denominator of 4040, multiply both the numerator and the denominator by 55. This gives us (5(3x5))/40(5*(3x-5))/40.
  3. Rewrite with common denominator: Rewrite the equation with the common denominator.\newlineNow that both fractions have the same denominator, the equation becomes:\newline(5(3x5))/40(3x9)/40=2(5*(3x-5))/40 - (3x-9)/40 = 2
  4. Combine fractions: Combine the fractions.\newlineSince the fractions have the same denominator, we can combine them:\newline(5(3x5)(3x9))/40=2(5(3x-5) - (3x-9))/40 = 2
  5. Eliminate denominator: Multiply both sides of the equation by 4040 to eliminate the denominator.\newline40×(5×(3x5)(3x9)40)=2×4040 \times \left(\frac{5\times(3x-5) - (3x-9)}{40}\right) = 2 \times 40\newlineThis simplifies to:\newline5×(3x5)(3x9)=805\times(3x-5) - (3x-9) = 80
  6. Distribute multiplication: Distribute the multiplication across the parentheses. 15x253x+9=8015x - 25 - 3x + 9 = 80
  7. Combine like terms: Combine like terms. 12x16=8012x - 16 = 80
  8. Isolate term with x: Add 1616 to both sides of the equation to isolate the term with xx.\newline12x16+16=80+1612x - 16 + 16 = 80 + 16\newlineThis simplifies to:\newline12x=9612x = 96
  9. Solve for x: Divide both sides by 1212 to solve for x.\newline12x12=9612\frac{12x}{12} = \frac{96}{12}\newlineThis simplifies to:\newlinex=8x = 8