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.

Tags

CCSS.7.EE.B.4A

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there are no values that can be substituted for the variable that will make the equation true.

Tags

CCSS.8.EE.C.7A

Front

What is the first step in solving the equation 12x - 8 = 12x - 9 - 1?

Back

The first step is to simplify both sides of the equation, which leads to -8 = -10, indicating no solution.

Tags

CCSS.8.EE.C.7A

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.

Tags

CCSS.6.EE.B.8

Front

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

Back

First, distribute: 2x - 2 < 8. Then add 2 to both sides: 2x < 10. Finally, divide by 2: x < 5.

Tags

CCSS.7.EE.B.4B

Front

What does it mean if an inequality has infinitely many solutions?

Back

It means that there are countless values that satisfy the inequality, often represented by a range of numbers.

Front

What is the solution to the inequality -3 - 6(4x + 6) > -111?

Back

First, simplify: -3 - 24x - 36 > -111. Combine like terms: -24x > -72. Divide by -24 (remember to flip the inequality): x < 3.

Front

What is the purpose of graphing an inequality?

Back

Graphing an inequality visually represents the set of solutions on a number line, showing which values satisfy the inequality.

Tags

CCSS.6.EE.B.8

Front

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

Back

First, subtract 5: 72 ≤ 8n. Then divide by 8: 9 ≤ n, or n ≥ 9.

Tags

CCSS.6.EE.B.8

Front

What is a common mistake when solving multistep equations?

Back

A common mistake is to incorrectly apply the distributive property or to forget to flip the inequality sign when multiplying or dividing by a negative number.