Equations with Algebra Tiles

Front

What are algebra tiles?

Back

Algebra tiles are physical or virtual manipulatives used to represent algebraic expressions and equations visually. They help in understanding concepts like addition, subtraction, and solving equations.

Front

How do you represent the expression 5x - 1 + 2x + 3 using algebra tiles?

Back

You would use 5 positive x-tiles, 2 additional positive x-tiles, 1 negative unit tile, and 3 positive unit tiles.

Front

What is the first step to solve the equation 8v - 4(v + 8) = 8?

Back

Distribute the -4 to both terms inside the parentheses: 8v - 4v - 32 = 8.

Front

What does it mean to combine like terms in an expression?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power, simplifying the expression.

Front

How do you solve the equation (2x - 3) / 4 = 9?

Back

Multiply both sides by 4 to eliminate the fraction: 2x - 3 = 36, then add 3 to both sides: 2x = 39, and finally divide by 2: x = 19.5.

Front

What is the solution to the equation 3x + 1 = x - 5?

Back

To solve, subtract x from both sides: 2x + 1 = -5, then subtract 1: 2x = -6, and divide by 2: x = -3.

Front

What does the expression 3(-x + 2) represent?

Back

It represents the distribution of 3 to both terms inside the parentheses, resulting in -3x + 6.

Front

What is the purpose of using algebra tiles in solving equations?

Back

Algebra tiles provide a visual representation that helps students understand the structure of equations and the process of solving them.

Front

How can you check if your solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is the significance of the equation 5x - 1 + 2x + 3 = 0?

Back

This equation can be solved to find the value of x that makes the expression equal to zero, which is important in understanding roots of equations.