Equations and Inequalities with Word problems

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or equal to the other. Examples include <, >, ≤, and ≥.

Front

What does the inequality k < 3 represent on a number line?

Back

It represents all numbers less than 3, which is shown by a line extending to the left of 3 on the number line.

Front

How do you solve the inequality 4x + 7 ≤ 23?

Back

Subtract 7 from both sides to get 4x ≤ 16, then divide by 4 to find x ≤ 4.

Front

What is the first step in solving the equation x + 16 = 50?

Back

Subtract 16 from both sides to isolate x, resulting in x = 34.

Front

If 472 students are going on a field trip and 120 are returning home, how do you find the number of students spending the night?

Back

Subtract 120 from 472 to find the number of students spending the night: 472 - 120 = 352.

Front

How do you determine the number of cabins needed if each cabin sleeps 8 people?

Back

Divide the number of students spending the night by the capacity of each cabin: 352 ÷ 8 = 44 cabins.

Front

What does the inequality r ≥ -6 mean?

Back

It means that r can be any number greater than or equal to -6, including -6 itself.

Front

What is the solution to the inequality 3x - 5 > 1?

Back

Add 5 to both sides to get 3x > 6, then divide by 3 to find x > 2.

Front

What is a word problem in mathematics?

Back

A word problem is a mathematical question presented in the form of a story or real-life scenario that requires translating the words into mathematical expressions or equations.

Front

How do you set up an equation from a word problem?

Back

Identify the unknown variable, translate the words into a mathematical expression, and set it equal to the known quantity.