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

Expand Equation: Expand the equation using the distributive property. -x + 2(x + 3) = 6 + x -x + 2*x + 2*3 = 6 + x -x + 2x + 6 = 6 + xCombine Like Terms: Combine like terms on the left side of the equation. -x + 2x + 6 = 6 + x (2x - x) + 6 = 6 + x x + 6 = 6 + xSubtract Variable: Since x is on both sides of the equation, subtract x from both sides to see if there is a solution. x + 6 - x = 6 + x - x 6 = 6Eliminate Variable: Observe that the variable x has been eliminated and we are left with a true statement, 6 = 6. This means that any value for x will satisfy the original equation, so the solution is all real numbers.

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Grade 8

Solve multi-step equations with fractional coefficients

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Q. Find the solution to this equation.

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-x+2(x+3)=6+x

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(A) No solution

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(B) All real numbers

Expand Equation: Expand the equation using the distributive property. $\newline$ $-x + 2(x + 3) = 6 + x$ $\newline$ $-x + 2\times x + 2\times 3 = 6 + x$ $\newline$ $-x + 2x + 6 = 6 + x$
Combine Like Terms: Combine like terms on the left side of the equation. $\newline$ $-x + 2x + 6 = 6 + x$ $\newline$ $(2x - x) + 6 = 6 + x$ $\newline$ $x + 6 = 6 + x$
Subtract Variable: Since $x$ is on both sides of the equation, subtract $x$ from both sides to see if there is a solution. $\newline$ $x + 6 - x = 6 + x - x$ $\newline$ $6 = 6$
Eliminate Variable: Observe that the variable $x$ has been eliminated and we are left with a true statement, $6 = 6$ . This means that any value for $x$ will satisfy the original equation, so the solution is all real numbers.