Equations with Combining Like Terms OR Distributive Property

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum or difference.

Front

How do you combine like terms in an expression?

Back

To combine like terms, identify terms that have the same variable raised to the same power and add or subtract their coefficients.

Front

What is the first step in solving an equation?

Back

The first step in solving an equation is to isolate the variable by performing inverse operations on both sides of the equation.

Front

How do you solve the equation -(n - 8) = -2?

Back

First, distribute the negative sign: -n + 8 = -2. Then, subtract 8 from both sides: -n = -10. Finally, multiply by -1: n = 10.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the solution to the equation 10 - 5x + 20 = 50?

Back

Combine like terms: 30 - 5x = 50. Subtract 30 from both sides: -5x = 20. Divide by -5: x = -4.

Front

How do you apply the Distributive Property to the expression 6(3x - 5)?

Back

Use the Distributive Property: 6 * 3x - 6 * 5 = 18x - 30.

Front

What is the result of combining the terms 3y + 4y + 6?

Back

Combine like terms: 3y + 4y = 7y, so the expression becomes 7y + 6.

Front

How do you solve the equation 6(3x - 5) - 7x = 25?

Back

Distribute: 18x - 30 - 7x = 25. Combine like terms: 11x - 30 = 25. Add 30 to both sides: 11x = 55. Divide by 11: x = 5.

Front

What is the solution to the equation -4(8 + 5n) = 8?

Back

Distribute: -32 - 20n = 8. Add 32 to both sides: -20n = 40. Divide by -20: n = -2.