5(1)/(3)*x-1=1(2)/(9)

Convert to Improper Fractions: Convert the mixed numbers to improper fractions. 5(1)/(3) can be converted to an improper fraction by multiplying the whole number 5 by the denominator 3 and adding the numerator 1, which gives us (5*3 + 1)/3 = 16/3. Similarly, 1(2)/(9) can be converted to an improper fraction by multiplying the whole number 1 by the denominator 9 and adding the numerator 2, which gives us (1*9 + 2)/9 = 11/9.Rewrite Using Improper Fractions: Rewrite the equation using the improper fractions. The equation now becomes (16/3)*x - 1 = 11/9.Isolate Term with x: To isolate the term with x, add 1 to both sides of the equation. (16/3)*x - 1 + 1 = 11/9 + 1 (16/3)*x = 11/9 + 9/9Simplify Right Side: Simplify the right side of the equation by adding the fractions. 11/9 + 9/9 = (11 + 9)/9 11/9 + 9/9 = 20/9 So, (16/3)*x = 20/9Solve for x: Solve for x by multiplying both sides of the equation by the reciprocal of (16/3). x = (20/9) * (3/16)Multiply Numerators and Denominators: Multiply the numerators and denominators. x = (20*3)/(9*16) x = 60/144Simplify the Fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 12. x = (60/12)/(144/12) x = 5/12

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$5 \frac{1}{3} \cdot x-1=1 \frac{2}{9}$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

5 \frac{1}{3} \cdot x-1=1 \frac{2}{9}

Convert to Improper Fractions: Convert the mixed numbers to improper fractions. $\newline$ $5\frac{1}{3}$ can be converted to an improper fraction by multiplying the whole number $5$ by the denominator $3$ and adding the numerator $1$ , which gives us $\frac{(5\times 3 + 1)}{3} = \frac{16}{3}$ . $\newline$ Similarly, $1\frac{2}{9}$ can be converted to an improper fraction by multiplying the whole number $1$ by the denominator $9$ and adding the numerator $2$ , which gives us $\frac{(1\times 9 + 2)}{9} = \frac{11}{9}$ .
Rewrite Using Improper Fractions: Rewrite the equation using the improper fractions. $\newline$ The equation now becomes $(\frac{16}{3})x - 1 = \frac{11}{9}$ .
Isolate Term with x: To isolate the term with x, add $1$ to both sides of the equation. $\newline$ $(\frac{16}{3})*x - 1 + 1 = \frac{11}{9} + 1$ $\newline$ $(\frac{16}{3})*x = \frac{11}{9} + \frac{9}{9}$
Simplify Right Side: Simplify the right side of the equation by adding the fractions. $\newline$ $\frac{11}{9} + \frac{9}{9} = \frac{11 + 9}{9}$ $\newline$ $\frac{11}{9} + \frac{9}{9} = \frac{20}{9}$ $\newline$ So, $\frac{16}{3}$ $x$ = $\frac{20}{9}$
Solve for x: Solve for x by multiplying both sides of the equation by the reciprocal of $(\frac{16}{3})$ . $x = (\frac{20}{9}) \times (\frac{3}{16})$
Multiply Numerators and Denominators: Multiply the numerators and denominators. $\newline$ $x = \frac{20 \times 3}{9 \times 16}$ $\newline$ $x = \frac{60}{144}$
Simplify the Fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $12$ . $x = \frac{60}{12}/\frac{144}{12}$ $x = \frac{5}{12}$