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Solve for x and write your answer in simplest form. 6x-(9x-(3)/(2))=-2(3x-(5)/(4))+2 Answer: x=

Solve for x x and write your answer in simplest form.\newline6x−(9x−32)=−2(3x−54)+2 6 x-\left(9 x-\frac{3}{2}\right)=-2\left(3 x-\frac{5}{4}\right)+2 \newlineAnswer: x= x=

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Q. Solve for x x and write your answer in simplest form.\newline6x−(9x−32)=−2(3x−54)+2 6 x-\left(9 x-\frac{3}{2}\right)=-2\left(3 x-\frac{5}{4}\right)+2 \newlineAnswer: x= x=
  1. Distribute and Simplify: First, we need to distribute the negative sign inside the parentheses on the left side of the equation and distribute −2-2 on the right side of the equation.\newline6x−9x+32=−2×3x+2×54+26x - 9x + \frac{3}{2} = -2 \times 3x + 2 \times \frac{5}{4} + 2
  2. Combine Like Terms: Now, let's simplify both sides of the equation by combining like terms. \newline−3x+32=−6x+52+2-3x + \frac{3}{2} = -6x + \frac{5}{2} + 2
  3. Convert and Combine Constants: Next, we convert 22 to a fraction with the same denominator as 52\frac{5}{2} to combine the constants on the right side.\newline−3x+32=−6x+52+42-3x + \frac{3}{2} = -6x + \frac{5}{2} + \frac{4}{2}
  4. Add/Subtract to Isolate x: Now, we combine the constants on the right side.\newline−3x+32=−6x+92-3x + \frac{3}{2} = -6x + \frac{9}{2}
  5. Combine Like Terms: Next, we add 6x6x to both sides to get all the xx terms on one side.\newline−3x+6x+32=−6x+6x+92-3x + 6x + \frac{3}{2} = -6x + 6x + \frac{9}{2}
  6. Isolate x Term: Simplify the equation by combining like terms. 3x+32=923x + \frac{3}{2} = \frac{9}{2}
  7. Simplify Constants: Now, we subtract 32\frac{3}{2} from both sides to isolate the xx term.\newline3x+32−32=92−323x + \frac{3}{2} - \frac{3}{2} = \frac{9}{2} - \frac{3}{2}
  8. Simplify Fraction: Simplify the equation by combining the constants. 3x=623x = \frac{6}{2}
  9. Solve for x: Simplify the fraction on the right side.\newline3x=33x = 3
  10. Final Answer: Finally, divide both sides by 33 to solve for xx.x=33x = \frac{3}{3}
  11. Final Answer: Finally, divide both sides by 33 to solve for xx. \newlinex=33x = \frac{3}{3} Simplify the fraction to get the final answer. \newlinex=1x = 1

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