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Solve the equation. Check your solution. 9[4-7(x-1)]+4[(2x+5)-7]=11 x-332 The solution set is _____. Type an integer or a simplified fraction.

Solve the equation. Check your solution.\newline9[4−7(x−1)]+4[(2x+5)−7]=11x−332 9[4-7(x-1)]+4[(2 x+5)-7]=11 x-332 \newlineThe solution set is _____\_\_\_\_\_. Type an integer or a simplified fraction.

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Full solution

Q. Solve the equation. Check your solution.\newline9[4−7(x−1)]+4[(2x+5)−7]=11x−332 9[4-7(x-1)]+4[(2 x+5)-7]=11 x-332 \newlineThe solution set is _____\_\_\_\_\_. Type an integer or a simplified fraction.
  1. Distribute and Simplify: Distribute the 99 into the first set of brackets and the 44 into the second set of brackets.\newline9[4−7(x−1)]+4[(2x+5)−7]9[4 - 7(x - 1)] + 4[(2x + 5) - 7]\newline=9[4−7x+7]+4[2x+5−7]= 9[4 - 7x + 7] + 4[2x + 5 - 7]\newline=36−63x+63+8x+20−28= 36 - 63x + 63 + 8x + 20 - 28
  2. Combine Like Terms: Combine like terms within the distributed results.\newline36−63x+63+8x+20−2836 - 63x + 63 + 8x + 20 - 28\newline= (36+63+20−28)+(−63x+8x)(36 + 63 + 20 - 28) + (-63x + 8x)\newline= 91−55x91 - 55x
  3. Rewrite Equation: Rewrite the equation with the simplified left side.\newline91−55x=11x−33291 - 55x = 11x - 332
  4. Add 55x55x to Both Sides: Add 55x55x to both sides of the equation to get all xx terms on one side.\newline91−55x+55x=11x−332+55x91 - 55x + 55x = 11x - 332 + 55x\newline91=66x−33291 = 66x - 332
  5. Add 332332 to Both Sides: Add 332332 to both sides of the equation to isolate the xx term.\newline91+332=66x−332+33291 + 332 = 66x - 332 + 332\newline423=66x423 = 66x
  6. Divide by 6666: Divide both sides by 6666 to solve for xx.42366=66x66\frac{423}{66} = \frac{66x}{66}x=6.409090909090909x = 6.409090909090909

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