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

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

Back

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

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that will satisfy the equation.

Front

How do you solve the equation 8v - 4(v + 8) = 8?

Back

1. Distribute: 8v - 4v - 32 = 8. 2. Combine like terms: 4v - 32 = 8. 3. Add 32 to both sides: 4v = 40. 4. Divide by 4: v = 10.

Front

What is the distributive property?

Back

A property that states a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you combine like terms in an equation?

Back

By adding or subtracting the coefficients of terms that have the same variable raised to the same power.

Front

What is the solution to the equation 4(-8x + 5) = -32x - 26?

Back

No solution, as both sides simplify to contradictory statements.

Front

What is the first step in solving 2x + 3(5x - 7) = 47?

Back

Distribute: 2x + 15x - 21 = 47.

Front

What does it mean to isolate a variable?

Back

To manipulate an equation so that the variable is on one side and all other terms are on the opposite side.