Multi-step equations

Front

What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, and division.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean if an equation has 'no solution'?

Back

An equation has 'no solution' when there are no values that can satisfy the equation, often resulting in a contradiction.

Front

What is the first step in solving the equation \( \frac{(2x + 12)}{4} = 12 \)?

Back

The first step is to multiply both sides of the equation by 4 to eliminate the fraction.

Front

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

Back

You can check your solution by substituting the value back into the original equation to see if both sides are equal.

Front

What is the solution to the equation \( x + 9 = x - 9 \)?

Back

The solution is 'no solution' because simplifying leads to a contradiction (9 = -9).

Front

What is the process to solve \( 8v - 4(v + 8) = 8 \)?

Back

First, distribute -4 to (v + 8), then combine like terms and isolate v.

Front

What does it mean to distribute in an equation?

Back

Distributing means multiplying a term outside the parentheses by each term inside the parentheses.

Front

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

Back

First, distribute the negative sign, then isolate n by adding 8 to both sides.

Front

What is the final step in solving \( \frac{(x + 12)}{6} = -4 \)?

Back

Multiply both sides by 6 to eliminate the fraction, then isolate x.