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Solve for x. {:[(3x-2)/(3x+1)=(1)/(3)],[x=]:}

Solve for x x .\newline3x−23x+1=13x= \begin{array}{l} \frac{3 x-2}{3 x+1}=\frac{1}{3} \\ x= \end{array}

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Full solution

Q. Solve for x x .\newline3x−23x+1=13x= \begin{array}{l} \frac{3 x-2}{3 x+1}=\frac{1}{3} \\ x= \end{array}
  1. Isolate the equation: First, let's isolate the equation that is already solved for xx.x=…x = \ldotsThis equation tells us that whatever xx is, it is equal to itself. This is a tautology and doesn't provide any new information, so we can ignore this part of the system and focus on the first equation.
  2. Cross-multiply to eliminate fractions: Now, let's solve the first equation (3x−2)/(3x+1)=1/3(3x-2)/(3x+1) = 1/3. To do this, we can cross-multiply to get rid of the fractions.\newline(3x−2)×3=(3x+1)×1(3x - 2) \times 3 = (3x + 1) \times 1
  3. Perform multiplication on both sides: Perform the multiplication on both sides of the equation. 9x−6=3x+19x - 6 = 3x + 1
  4. Rearrange the equation: Next, we want to get all the xx terms on one side and the constants on the other side. We can do this by subtracting 3x3x from both sides and adding 66 to both sides.9x−6−3x=3x+1−3x9x - 6 - 3x = 3x + 1 - 3x9x−3x−6+6=1+69x - 3x - 6 + 6 = 1 + 6
  5. Simplify both sides: Simplify both sides of the equation. 6x=76x = 7
  6. Divide both sides to solve for xx: Finally, divide both sides by 66 to solve for xx.x=76x = \frac{7}{6}

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