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Solve the following equation for x. Express your answer in the simplest form. -2(3x-1)=-6x+2

Solve the following equation for x x . Express your answer in the simplest form.\newline−2(3x−1)=−6x+2 -2(3 x-1)=-6 x+2 \newline

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Full solution

Q. Solve the following equation for x x . Express your answer in the simplest form.\newline−2(3x−1)=−6x+2 -2(3 x-1)=-6 x+2 \newline
  1. Distribute −2-2: First, distribute the −2-2 across the terms inside the parentheses on the left side of the equation.−2×3x=−6x-2 \times 3x = -6x−2×−1=2-2 \times -1 = 2So the equation becomes:−6x+2=−6x+2-6x + 2 = -6x + 2
  2. Identify Same Terms: Next, observe that both sides of the equation have the same terms, −6x+2-6x + 2. This suggests that the equation is true for all values of xx, meaning the solution is all real numbers.
  3. Final Solution: Since the equation simplifies to 0=00 = 0 after subtracting −6x+2-6x + 2 from both sides, there is no need to perform any further operations. The solution is all real numbers.

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