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Solve the following equation for x. Express your answer in the simplest form. 9(-8x+2)-9=-5-(3)/(2)(-6x-10)

Solve the following equation for x x . Express your answer in the simplest form.\newline9(−8x+2)−9=−5−32(−6x−10) 9(-8 x+2)-9=-5-\frac{3}{2}(-6 x-10) \newline

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Full solution

Q. Solve the following equation for x x . Express your answer in the simplest form.\newline9(−8x+2)−9=−5−32(−6x−10) 9(-8 x+2)-9=-5-\frac{3}{2}(-6 x-10) \newline
  1. Combine Like Terms: Now, combine like terms on the left side.\newline−72x+9=−5−(32)(−6x−10)-72x + 9 = -5 - \left(\frac{3}{2}\right)(-6x - 10)
  2. Distribute on Right Side: Next, distribute the (3/2)(3/2) on the right side of the equation.\newline−72x+9=−5−(32)(−6x)−(32)(−10)-72x + 9 = -5 - \left(\frac{3}{2}\right)(-6x) - \left(\frac{3}{2}\right)(-10)\newline−72x+9=−5+9x+15-72x + 9 = -5 + 9x + 15
  3. Combine Like Terms: Combine like terms on the right side.\newline−72x+9=9x+10-72x + 9 = 9x + 10
  4. Add 72x72x to Both Sides: Now, add 72x72x to both sides to get all xx terms on one side.\newline−72x+72x+9=9x+72x+10-72x + 72x + 9 = 9x + 72x + 10\newline9=81x+109 = 81x + 10
  5. Subtract 1010: Subtract 1010 from both sides to isolate the xx term.\newline9−10=81x+10−109 - 10 = 81x + 10 - 10\newline−1=81x-1 = 81x
  6. Divide by 8181: Finally, divide both sides by 8181 to solve for xx.−181=81x81-\frac{1}{81} = \frac{81x}{81}x=−181x = -\frac{1}{81}

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