(5)/(4)(4a+2)=1(5)/(6)

Clear Fractions: First, we need to simplify the equation by getting rid of the fractions. To do this, we can find a common denominator and multiply both sides of the equation by that common denominator to eliminate the fractions. The common denominator for 4 and 6 is 12, so we multiply both sides of the equation by 12 to clear the fractions. (5/4)(4a+2) * 12 = (1 5/6) * 12Distribute and Simplify: Now, we distribute the 12 on the left side of the equation to both terms inside the parentheses and simplify the right side of the equation. (5 * 12 / 4)(4a+2) = (1 * 6 + 5/6) * 12Continue Simplifying: Simplify both sides of the equation by performing the arithmetic operations. (5 * 3)(4a+2) = (6 + 5/6) * 12Convert to Improper Fraction: Continue simplifying by multiplying the numbers. 15(4a+2) = (6 5/6) * 12Multiply by 12: Convert 6 5/6 to an improper fraction to make multiplication easier. 15(4a+2) = (41/6) * 12Complete Multiplication: Multiply the fraction by 12. 15(4a+2) = 41 * 2Distribute 15: Complete the multiplication on the right side of the equation. 15(4a+2) = 82Subtract 30: Now, distribute the 15 on the left side of the equation. 60a + 30 = 82Perform Subtraction: Subtract 30 from both sides of the equation to isolate the term with the variable 'a'. 60a = 82 - 30Divide by 60: Perform the subtraction to find the value of 60a. 60a = 52Simplify Fraction: Finally, divide both sides of the equation by 60 to solve for 'a'. a = 52 / 60Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4. a = 13 / 15

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$\frac{5}{4}(4 a+2)=1 \frac{5}{6}$

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Algebra 1

Multiplication with rational exponents

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\frac{5}{4}(4 a+2)=1 \frac{5}{6}

$\newline$ $\newline$
Distribute and Simplify: Now, we distribute the $12$ on the left side of the equation to both terms inside the parentheses and simplify the right side of the equation. $\newline$ $(5 \times 12 / 4)(4a+2) = (1 \times 6 + 5/6) \times 12$
Continue Simplifying: Simplify both sides of the equation by performing the arithmetic operations. $\newline$ $(5 \times 3)(4a+2) = (6 + \frac{5}{6}) \times 12$
Convert to Improper Fraction: Continue simplifying by multiplying the numbers. $\newline$ $15(4a+2) = \left(6 \frac{5}{6}\right) \times 12$
Multiply by $12$ : Convert $6 \frac{5}{6}$ to an improper fraction to make multiplication easier. $\newline$ $15(4a+2) = \left(\frac{41}{6}\right) \times 12$
Complete Multiplication: Multiply the fraction by $12$ . $\newline$ $15(4a+2) = 41 \times 2$
Distribute $15$ : Complete the multiplication on the right side of the equation. $15(4a+2) = 82$
Subtract $30$ : Now, distribute the $15$ on the left side of the equation. $\newline$ $60a + 30 = 82$
Perform Subtraction: Subtract $30$ from both sides of the equation to isolate the term with the variable ' $a$ '. $\newline$ $60a = 82 - 30$
Divide by $60$ : Perform the subtraction to find the value of $60a$ . $\newline$ $60a = 52$
Simplify Fraction: Finally, divide both sides of the equation by $60$ to solve for ' $a$ '. $\newline$ $a = \frac{52}{60}$
Simplify Fraction: Finally, divide both sides of the equation by $60$ to solve for ' $a$ '. $\newline$ $a = \frac{52}{60}$ Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $4$ . $\newline$ $a = \frac{13}{15}$