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Find the solution to this equation. -x+2(x+3)=6+x (A) No solution (B) All real numbers

Find the solution to this equation.\newline−x+2(x+3)=6+x-x+2(x+3)=6+x\newline(A) No solution\newline(B) All real numbers

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Solve multi-step equations with fractional coefficientsright chevron icon

Full solution

Q. Find the solution to this equation.\newline−x+2(x+3)=6+x-x+2(x+3)=6+x\newline(A) No solution\newline(B) All real numbers
  1. Expand Equation: Expand the equation using the distributive property.\newline−x+2(x+3)=6+x-x + 2(x + 3) = 6 + x\newline−x+2×x+2×3=6+x-x + 2\times x + 2\times 3 = 6 + x\newline−x+2x+6=6+x-x + 2x + 6 = 6 + x
  2. Combine Like Terms: Combine like terms on the left side of the equation.\newline−x+2x+6=6+x-x + 2x + 6 = 6 + x\newline(2x−x)+6=6+x(2x - x) + 6 = 6 + x\newlinex+6=6+xx + 6 = 6 + x
  3. Subtract Variable: Since xx is on both sides of the equation, subtract xx from both sides to see if there is a solution.\newlinex+6−x=6+x−xx + 6 - x = 6 + x - x\newline6=66 = 6
  4. Eliminate Variable: Observe that the variable xx has been eliminated and we are left with a true statement, 6=66 = 6. This means that any value for xx will satisfy the original equation, so the solution is all real numbers.

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