Questions: Solve the equation and check the solution. If applicable, tell whether the equation is an identity or a contradiction. -9x+6-5(x-1)=-5x-(8x-3)+5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type an integer or a simplified fraction.) B. The solution set is all real numbers, so the equation is an identity. C. The solution set is ∅, so the equation is a contradiction.

Solution Steps

First, we simplify both sides of the given equation: \[ -9x + 6 - 5(x - 1) = -5x - (8x - 3) + 5 \]

Distribute and combine like terms: \[ -9x + 6 - 5x + 5 = -5x - 8x + 3 + 5 \]

Simplify further: \[ -14x + 11 = -13x + 8 \]

Next, we isolate the variable \(x\) by moving terms with \(x\) to one side and constant terms to the other side: \[ -14x + 11 = -13x + 8 \]

Add \(13x\) to both sides: \[ -14x + 13x + 11 = 8 \]

Combine like terms: \[ -x + 11 = 8 \]

Subtract 11 from both sides: \[ -x = 8 - 11 \]

Simplify: \[ -x = -3 \]

Multiply both sides by -1: \[ x = 3 \]

Substitute \(x = 3\) back into the original equation to verify: \[ -9(3) + 6 - 5(3 - 1) = -5(3) - (8(3) - 3) + 5 \]

Simplify both sides: \[ -27 + 6 - 5(2) = -15 - (24 - 3) + 5 \] \[ -27 + 6 - 10 = -15 - 21 + 5 \] \[ -31 = -31 \]

Since both sides are equal, \(x = 3\) is a valid solution.

Final Answer