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Solve for
x.

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

Solve for $\mathrm{x}$ . $\newline$ $\frac{3 x-5}{8}-\frac{3 x-9}{40}=2$ $\newline$ Answer:

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Solve two-step equations with parentheses

Full solution

Q. Solve for

\mathrm{x}

.

\newline

\frac{3 x-5}{8}-\frac{3 x-9}{40}=2

\newline

Answer:

Find common denominator: Find a common denominator for the fractions. $\newline$ 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. $\newline$ Now that both fractions have the same denominator, the equation becomes: $\newline$ $(5*(3x-5))/40 - (3x-9)/40 = 2$
Combine fractions: Combine the fractions. $\newline$ Since the fractions have the same denominator, we can combine them: $\newline$ $(5(3x-5) - (3x-9))/40 = 2$
Eliminate denominator: Multiply both sides of the equation by $40$ to eliminate the denominator. $\newline$ $40 \times \left(\frac{5\times(3x-5) - (3x-9)}{40}\right) = 2 \times 40$ $\newline$ This simplifies to: $\newline$ $5\times(3x-5) - (3x-9) = 80$
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 $x$ . $\newline$ $12x - 16 + 16 = 80 + 16$ $\newline$ This simplifies to: $\newline$ $12x = 96$
Solve for x: Divide both sides by $12$ to solve for x. $\newline$ $\frac{12x}{12} = \frac{96}{12}$ $\newline$ This simplifies to: $\newline$ $x = 8$

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