Find common denominator: Find a common denominator for the fractions.The denominators are 8 and 40. The least common denominator (LCD) for 8 and 40 is 40.
Convert first fraction: Convert the first fraction to have the common denominator of 40. To convert (3x−5)/8 to a fraction with a denominator of 40, multiply both the numerator and the denominator by 5. This gives us (5∗(3x−5))/40.
Rewrite with common denominator: Rewrite the equation with the common denominator.Now that both fractions have the same denominator, the equation becomes:(5∗(3x−5))/40−(3x−9)/40=2
Combine fractions: Combine the fractions.Since the fractions have the same denominator, we can combine them:(5(3x−5)−(3x−9))/40=2
Eliminate denominator: Multiply both sides of the equation by 40 to eliminate the denominator.40×(405×(3x−5)−(3x−9))=2×40This simplifies to:5×(3x−5)−(3x−9)=80
Distribute multiplication: Distribute the multiplication across the parentheses. 15x−25−3x+9=80
Combine like terms: Combine like terms. 12x−16=80
Isolate term with x: Add 16 to both sides of the equation to isolate the term with x.12x−16+16=80+16This simplifies to:12x=96
Solve for x: Divide both sides by 12 to solve for x.1212x=1296This simplifies to:x=8
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