7/3(1/2x - 10/3) = -35/3 - 1/2x

Distribute and Simplify: First, distribute 7/3 to both terms inside the parentheses. 7/3 * (1/2x - 10/3) = -35/3 - 1/2x (7/3 * 1/2x) - (7/3 * 10/3) = -35/3 - 1/2x 7/6x - 70/9 = -35/3 - 1/2xCombine Like Terms: Next, combine like terms by adding 1/2x to both sides of the equation. 7/6x - 70/9 + 1/2x = -35/3 - 1/2x + 1/2x To combine 7/6x and 1/2x, find a common denominator, which is 6. (7/6x + 3/6x) - 70/9 = -35/3 10/6x - 70/9 = -35/3Simplify Fraction: Now, simplify the fraction 10/6x by dividing both numerator and denominator by 2. (10/6x) / (2/2) = 5/3x 5/3x - 70/9 = -35/3Isolate Variable Term: Next, to isolate the variable term, add 70/9 to both sides of the equation. 5/3x - 70/9 + 70/9 = -35/3 + 70/9 5/3x = -35/3 + 70/9 To combine -35/3 and 70/9, find a common denominator, which is 9. 5/3x = (-105/9) + 70/9 5/3x = -35/9Solve for x: Finally, solve for x by multiplying both sides by the reciprocal of 5/3. 5/3x * 3/5 = -35/9 * 3/5 x = (-35 * 3) / (9 * 5) x = -105 / 45 x = -7/3

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$\frac{7}{3}(\frac{1}{2}x - \frac{10}{3}) = \frac{-35}{3} - \frac{1}{2}x$

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Math Problems

Grade 8

Solve multi-step equations with fractional coefficients

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\frac{7}{3}(\frac{1}{2}x - \frac{10}{3}) = \frac{-35}{3} - \frac{1}{2}x

Distribute and Simplify: First, distribute $\frac{7}{3}$ to both terms inside the parentheses. $\frac{7}{3} \times (\frac{1}{2}x - \frac{10}{3}) = -\frac{35}{3} - \frac{1}{2}x$ $\left(\frac{7}{3} \times \frac{1}{2}x\right) - \left(\frac{7}{3} \times \frac{10}{3}\right) = -\frac{35}{3} - \frac{1}{2}x$ $\frac{7}{6}x - \frac{70}{9} = -\frac{35}{3} - \frac{1}{2}x$
Combine Like Terms: Next, combine like terms by adding $\frac{1}{2}x$ to both sides of the equation. $\newline$ $\frac{7}{6}x - \frac{70}{9} + \frac{1}{2}x = -\frac{35}{3} - \frac{1}{2}x + \frac{1}{2}x$ $\newline$ To combine $\frac{7}{6}x$ and $\frac{1}{2}x$ , find a common denominator, which is $6$ . $\newline$ $(\frac{7}{6}x + \frac{3}{6}x) - \frac{70}{9} = -\frac{35}{3}$ $\newline$ $\frac{10}{6}x - \frac{70}{9} = -\frac{35}{3}$
Simplify Fraction: Now, simplify the fraction $\frac{10}{6x}$ by dividing both numerator and denominator by $2$ . $\left(\frac{10}{6x}\right) / \left(\frac{2}{2}\right) = \frac{5}{3x}$ $\frac{5}{3x} - \frac{70}{9} = -\frac{35}{3}$
Isolate Variable Term: Next, to isolate the variable term, add $\frac{70}{9}$ to both sides of the equation. $\newline$ $\frac{5}{3}x - \frac{70}{9} + \frac{70}{9} = -\frac{35}{3} + \frac{70}{9}$ $\newline$ $\frac{5}{3}x = -\frac{35}{3} + \frac{70}{9}$ $\newline$ To combine $-\frac{35}{3}$ and $\frac{70}{9}$ , find a common denominator, which is $9$ . $\newline$ $\frac{5}{3}x = (-\frac{105}{9}) + \frac{70}{9}$ $\newline$ $\frac{5}{3}x = -\frac{35}{9}$
Solve for x: Finally, solve for x by multiplying both sides by the reciprocal of $\frac{5}{3}$ . $\frac{5}{3}x \times \frac{3}{5} = \frac{-35}{9} \times \frac{3}{5}$ $x = \frac{(-35 \times 3)}{(9 \times 5)}$ $x = \frac{-105}{45}$ $x = \frac{-7}{3}$