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How many solutions does the following equation have? -6(x+7)=-4x-2 Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions

How many solutions does the following equation have?\newline−6(x+7)=−4x−2-6(x+7)=-4x-2\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions

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Q. How many solutions does the following equation have?\newline−6(x+7)=−4x−2-6(x+7)=-4x-2\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
  1. Distribute −6 -6 : Distribute −6 -6 to both terms inside the parentheses.−6(x+7)=−6×x+(−6)×7 -6(x+7) = -6\times x + (-6)\times 7 =−6x−42 = -6x - 42
  2. Rewrite with distributed terms: Rewrite the equation with the distributed terms.\newline−6x−42=−4x−2-6x - 42 = -4x - 2
  3. Add 6x6x to both sides: Add 6x6x to both sides of the equation to get the x terms on one side.\newline−6x+6x−42=−4x+6x−2-6x + 6x - 42 = -4x + 6x - 2\newline0−42=2x−20 - 42 = 2x - 2
  4. Simplify both sides: Simplify both sides of the equation. −42=2x−2-42 = 2x - 2
  5. Add 22 to isolate x: Add 22 to both sides of the equation to isolate the term with x.\newline−42+2=2x−2+2-42 + 2 = 2x - 2 + 2\newline−40=2x-40 = 2x
  6. Divide both sides by 22: Divide both sides by 22 to solve for xx.−40/2=2x/2-40 / 2 = 2x / 2−20=x-20 = x
  7. Check the solution: Check the solution by substituting xx back into the original equation.\newline−6(−20+7)=−4(−20)−2-6(-20 + 7) = -4(-20) - 2\newline−6(−13)=80−2-6(-13) = 80 - 2\newline78=7878 = 78

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