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

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

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 to graph an inequality?

Back

Graphing an inequality involves representing the solutions of the inequality on a number line, using open or closed circles to indicate whether endpoints are included.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to.

Front

How do you solve the inequality 2(x - 1) < 8?

Back

1. Distribute: 2x - 2 < 8. 2. Add 2: 2x < 10. 3. Divide by 2: x < 5.

Front

What is the solution to the inequality 77 ≤ 5 + 8n?

Back

1. Subtract 5: 72 ≤ 8n. 2. Divide by 8: 9 ≤ n or n ≥ 9.

Front

How do you solve -3 - 6(4x + 6) > -111?

Back

1. Distribute: -3 - 24x - 36 > -111. 2. Combine: -24x - 39 > -111. 3. Add 39: -24x > -72. 4. Divide by -24 (reverse inequality): x < 3.

Front

What is the solution to 6x + 10 > 5x - 12?

Back

1. Subtract 5x: x + 10 > -12. 2. Subtract 10: x > -22.

Front

What is a common error when solving equations?

Back

A common error is misapplying the distributive property or incorrectly handling negative signs.