Question

1. identify the errors in the equation. explain what the errors is/are and show how to solve the equation correctly.

(2x + 5) - (5x + 4) = 6 - 2(x - 3)
2x + 5 - 5x + 4 = 6 - 2x - 6
-3x + 9 = -2x
9 = x

Explanation:

Step1: Identify sign error 1

When distributing the negative sign to $(5x+4)$, it should be $-5x - 4$, not $-5x + 4$.

Step2: Identify sign error 2

When distributing $-2$ to $(x-3)$, it should be $-2x + 6$, not $-2x - 6$.

Step3: Rewrite equation correctly

$$(2x+5)-(5x+4)=6-2(x-3)$$
$$2x + 5 - 5x - 4 = 6 - 2x + 6$$

Step4: Simplify both sides

Combine like terms on left: $-3x + 1$
Combine like terms on right: $12 - 2x$
Equation: $-3x + 1 = 12 - 2x$

Step5: Isolate $x$ term

Add $3x$ to both sides:
$$1 = 12 + x$$

Step6: Solve for $x$

Subtract 12 from both sides:
$$x = 1 - 12$$

Answer:

Original errors:

1. Incorrect distribution of the negative sign: $(2x+5)-(5x+4)$ was simplified to $2x+5-5x+4$ instead of $2x+5-5x-4$.
2. Incorrect distribution of $-2$: $-2(x-3)$ was simplified to $-2x-6$ instead of $-2x+6$.

Correct solution: $x = -11$