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Solve the following equation for x. Express your answer in the simplest form. 10 x+9(2x+1)=-7(-4x-2)-5

Solve the following equation for x x . Express your answer in the simplest form.\newline10x+9(2x+1)=−7(−4x−2)−5 10 x+9(2 x+1)=-7(-4 x-2)-5 \newline

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Q. Solve the following equation for x x . Express your answer in the simplest form.\newline10x+9(2x+1)=−7(−4x−2)−5 10 x+9(2 x+1)=-7(-4 x-2)-5 \newline
  1. Distribute and Expand: First, distribute the 99 into (2x+1)(2x + 1).10x+9×2x+9×1=−7(−4x−2)−510x + 9 \times 2x + 9 \times 1 = -7(-4x - 2) - 510x+18x+9=−7(−4x−2)−510x + 18x + 9 = -7(-4x - 2) - 5
  2. Combine Like Terms: Combine like terms on the left side.\newline(10x+18x)+9=−7(−4x−2)−5(10x + 18x) + 9 = -7(-4x - 2) - 5\newline28x+9=−7(−4x−2)−528x + 9 = -7(-4x - 2) - 5
  3. Distribute Again: Now distribute the −7-7 into (−4x−2)(-4x - 2).28x+9=−7×−4x+−7×−2−528x + 9 = -7 \times -4x + -7 \times -2 - 528x+9=28x+14−528x + 9 = 28x + 14 - 5
  4. Combine Like Terms: Combine like terms on the right side.\newline28x+9=28x+14−528x + 9 = 28x + 14 - 5\newline28x+9=28x+928x + 9 = 28x + 9
  5. Isolate x Terms: Subtract 28x28x from both sides to get the x terms on one side.\newline28x+9−28x=28x+9−28x28x + 9 - 28x = 28x + 9 - 28x\newline9=99 = 9
  6. Final Solution: Since 9=99 = 9 is a true statement and there are no xx terms left, the equation is true for all xx. This means the solution is all real numbers.

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