Multi-step Equations

Front

What is a multi-step equation?

Back

An equation that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, and division.

Front

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

Back

1. Distribute: 3x + 8x - 8 = 3. 2. Combine like terms: 11x - 8 = 3. 3. Add 8 to both sides: 11x = 11. 4. Divide by 11: x = 1.

Front

Which equation has no solution?

Back

3(2x+1) = 6x+1, because it simplifies to 3 = 1, which is a contradiction.

Front

What is the first step in solving 2a - 4(a - 5) = 10?

Back

Distribute -4 to a and -5: 2a - 4a + 20 = 10.

Front

Solve the equation 7x - 4 = 3 + 8x.

Back

x = -7.

Front

What does it mean to combine like terms?

Back

To add or subtract terms that have the same variable raised to the same power.

Front

What is the distributive property?

Back

a(b + c) = ab + ac; it allows you to multiply a single term by two or more terms inside a parenthesis.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to get the variable alone on one side of the equation.

Front

What is the solution to the equation 15x - 30 = 0?

Back

x = 2.

Front

What is an equation with infinitely many solutions?

Back

An equation that simplifies to a true statement, like 0 = 0.