Writing Inequalities from Word Problems

What is an inequality?

• 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.

• A type of equation that has no solution.

• A graphical representation of a function.

• A statement that asserts the equality of two expressions.

What does the symbol '≤' mean in an inequality?

• 'Greater than'

• 'Less than'

• 'Less than or equal to'

• 'Equal to'

What is a solution set in the context of inequalities?

• A solution set is the set of all values that satisfy the inequality.

• A solution set is a single value that makes the inequality true.

• A solution set is the graphical representation of the inequality.

• A solution set is the range of values that do not satisfy the inequality.

What is the first step in solving an inequality?

• Isolate the variable on one side of the inequality.

• Add the same number to both sides of the inequality.

• Multiply both sides by a negative number.

• Graph the inequality on a number line.

How do you write an inequality from a word problem?

• Identify the quantities involved, determine the relationship between them, and express that relationship using inequality symbols.

• Write down the numbers mentioned in the problem and add them together.

• Convert the word problem into a linear equation and solve for x.

• Ignore the context and choose any random inequality.

In the problem, 'The seventh grade class needs to raise at least $1000 after renting a hall for $700. Each ticket costs $15. Write the inequality.'

• 15t + 700 ≥ 1000

• 15t - 700 ≥ 1000

• 15t + 700 ≤ 1000

• 15t - 700 ≤ 1000

In the problem, 'Tina's hair is 7 inches long and grows 0.5 inches a month. How many months will it take for her hair to be more than 20 inches long?' Write the inequality.

• 0.5m + 7 > 20

• 0.5m + 7 < 20

• 0.5m - 7 > 20

• 0.5m + 7 = 20

What does the symbol '<' mean in an inequality?

• 'greater than'

• 'equal to'

• 'less than'

• 'not equal to'

In the problem, 'Ross and Chandler have $14 and spend $3.50 on sodas. Each taco costs $1.75. How many tacos can they buy?' Write the inequality.

• 1.75t + 3.50 ≤ 14

• 1.75t + 3.50 < 14

• 1.75t - 3.50 ≤ 14

• 1.75t + 3.50 = 14

What is the difference between an equation and an inequality?

• An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

• An equation is a mathematical statement that contains a variable, while an inequality does not.

• An equation can only have one solution, while an inequality can have multiple solutions.

• An equation is always true, while an inequality can be false.