Solving Multistep Equations and Inequalities

Front

What is a multistep equation?

Back

A multistep 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, perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean for an equation to have no solution?

Back

An equation has no solution when there is no value for the variable that makes the equation true, often resulting in a contradiction.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

How do you graph an inequality on a number line?

Back

To graph an inequality, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate direction on the number line.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the endpoint, while a non-strict inequality (≤ or ≥) includes the endpoint.

Front

What is the first step in solving the inequality 6x + 10 > 5x - 12?

Back

The first step is to subtract 5x from both sides to begin isolating the variable x.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable that make the equation true.

Front

What is a solution set?

Back

A solution set is the set of all values that satisfy a given equation or inequality.

Front

How do you check if a solution is correct for an equation?

Back

To check a solution, substitute the value back into the original equation to see if both sides are equal.