Question

1. which one doesnt belong? identify the linear expression that does not belong with the other three. explain your reasoning.

a. $(-5x + 3) - (-7x - 1)$
b. $(-3x + 3) - (-5x - 2)$
c. $(x - 6) - (-x - 10)$
d. $(-7x + 2) - (-9x - 2)$

1. find the error a student simplified the expression $(5x - 7) - (-x + 2)$ to $7x + 3$. find the student’s error and correct it.
2. identify structure write two linear expressions that have a difference of $x + 1$
3. identify structure which linear expression would you need to subtract from $(5x + 3)$ to have a difference of $4x - x$

Explanation:

Step1: Simplify expression a

$(-5x + 3) - (-7x - 1) = -5x + 3 + 7x + 1 = 2x + 4$

Step2: Simplify expression b

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

Step3: Simplify expression c

$(x - 6) - (-x - 10) = x - 6 + x + 10 = 2x + 4$

Step4: Simplify expression d

$(-7x + 2) - (-9x - 2) = -7x + 2 + 9x + 2 = 2x + 4$

Step5: Identify the outlier

Expressions a, c, d simplify to $2x+4$, while b simplifies to $2x+5$.

(Problem 16):

Step1: Define the structure

Let the two linear expressions be $E_1$ and $E_2$, so $E_1 - E_2 = x + 1$.

Step2: Choose base expressions

Let $E_1 = 2x + 3$, solve for $E_2$:
$E_2 = E_1 - (x + 1) = (2x + 3) - (x + 1) = x + 2$

(Problem 17):

Step1: Set up the equation

Let the unknown expression be $E$. We know $(5x + 3) - E = -2$.

Step2: Solve for E

Rearrange: $E = (5x + 3) - (-2) = 5x + 3 + 2 = 5x + 5$

(Problem 19):

Step1: Simplify the correct expression

$(5x - 2) - (-x + 5) = 5x - 2 + x - 5 = 6x - 7$

Step2: Identify the student's error

The student incorrectly distributed the negative sign: they added $x$ but added $5$ instead of subtracting $5$, and miscalculated the coefficient of $x$.

Answer:

Expression b: $(-3x + 3) - (-5x - 2)$ does not belong. When simplified, expressions a, c, and d all equal $2x + 4$, but expression b simplifies to $2x + 5$.

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