Solving Equations with Vince the Variable

Vocabulary practice flashcards covering the core three-step equation solving procedure, key algebraic concepts, the Vince the Variable metaphor, and worked equation examples.

Vince the Variable

An introverted character representing the variable in an equation who prefers to be inside his house completely alone.

The Door (Metaphor)

The visual representation of the equals sign ($=$) in an equation, separating Vince's house from the outside where he wants all other numbers to go.

Inverse Operations

Opposite mathematical operations (such as dividing when a number is multiplying) used to move numbers away from the variable across the equals sign.

The Mission

To help Vince kick everyone out of his house by doing the opposite of what they want so he can be left alone.

Step 1 of Solving Equations

Identify and combine like terms.

Step 2 of Solving Equations

Use inverse operations to isolate the term with the variable.

Step 3 of Solving Equations

Use an inverse operation to isolate the variable itself.

Solution to $4x + 7 + 2x = 25$

Combine like terms to get $6x + 7 = 25$, subtract $7$ from both sides to get $6x = 18$, and divide by $6$ to obtain $x = 3$.

Solution to $3(m + 4) + 2m = 27$

Distribute $3$ to get $3m + 12 + 2m = 27$, combine like terms to get $5m + 12 = 27$, subtract $12$ to get $5m = 15$, and divide by $5$ to obtain $m = 3$.

Solution to $8y - 3 - 3y + 11 = 33$

Combine like terms to get $5y + 8 = 33$, subtract $8$ from both sides to get $5y = 25$, and divide by $5$ to obtain $y = 5$.

Solution to $5(2k - 1) - 4k + 9 = 22$

Distribute $5$ to get $10k - 5 - 4k + 9 = 22$, combine like terms to get $6k + 4 = 22$, subtract $4$ to get $6k = 18$, and divide by $6$ to obtain $k = 3$.

Equation Practice: $3x + 2 - 4x + 7 = -18$

A practice equation solved by identifying and combining the like terms $3x - 4x$ and $2 + 7$, followed by using inverse operations to isolate the variable term and the variable.