Question

name
8th grade
due: friday
homework
monday/tuesday

1. directions:

a. simplify the equation by using simplification moves.
b. record your steps below.
c. find the value of x if possible.
d. state which type of solution you get.

(image of algebraic tiles representing an equation)
wednesday/thursday
type of solution:
(table with columns for original equation, etc.)

Explanation:

Step1: Translate to equation

Gray squares = $x$, white squares = $-1$, so:
Left side: $2x + 3(-1)$; Right side: $x + 2(-1)$
Equation: $2x - 3 = x - 2$

Step2: Isolate $x$ (subtract $x$)

$2x - x - 3 = x - x - 2$
$\implies x - 3 = -2$

Step3: Solve for $x$ (add 3)

$x - 3 + 3 = -2 + 3$
$\implies x = 1$

Step4: Identify solution type

One unique value for $x$, so it is a one-solution equation.

Answer:

Original Equation: $2x - 3 = x - 2$
Steps:

1. Translate model to equation: $2x - 3 = x - 2$
2. Subtract $x$ from both sides: $x - 3 = -2$
3. Add 3 to both sides: $x = 1$

Value of $x$: $1$
Type of Solution: One unique solution