Writing Equations and Inequalities

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

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 represent a situation with an equation?

Back

To represent a situation with an equation, identify the quantities involved, define variables for unknowns, and express the relationship between them using mathematical symbols.

Front

What does the equation 7 + 9x = 30 represent in a real-world context?

Back

This equation represents a scenario where 7 feet of ribbon is cut from a 30-foot piece, and the remaining ribbon is divided into 9 equal lengths.

Front

How do you solve the equation 7 + 9x = 30 for x?

Back

To solve for x, subtract 7 from both sides to get 9x = 23, then divide both sides by 9 to find x = 23/9.

Front

What is the meaning of the inequality 15 + 6x ≤ 100?

Back

This inequality indicates that the total cost of $15 plus $6 per person must be less than or equal to $100.

Front

How do you solve the inequality 15 + 6x ≤ 100 for x?

Back

To solve for x, subtract 15 from both sides to get 6x ≤ 85, then divide both sides by 6 to find x ≤ 85/6.

Front

What does the expression (1/2)x - 4 ≥ 12 represent?

Back

This expression represents a situation where half of a number, decreased by 4, is greater than or equal to 12.

Front

How do you solve the inequality (1/2)x - 4 ≥ 12 for x?

Back

To solve for x, add 4 to both sides to get (1/2)x ≥ 16, then multiply both sides by 2 to find x ≥ 32.

Front

What is the significance of defining variables in word problems?

Back

Defining variables helps to translate a word problem into a mathematical equation or inequality, making it easier to solve.