Two-Step Inequality Word Problems

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. It typically involves adding or subtracting a number and then multiplying or dividing by another number.

Front

How do you represent a word problem as an inequality?

Back

To represent a word problem as an inequality, identify the quantities involved, determine the relationship (greater than, less than, etc.), and translate the words into mathematical symbols.

Front

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

Back

'>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

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

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left side is either larger than or equal to the value on the right side.

Front

How do you solve a two-step inequality?

Back

To solve a two-step inequality, perform the inverse operations in reverse order: first, isolate the term with the variable by adding or subtracting, then divide or multiply to solve for the variable.

Front

What is the first step in solving the inequality 25 - 2x > 10?

Back

The first step is to isolate the term with the variable by subtracting 25 from both sides, resulting in -2x > -15.

Front

In the context of word problems, what does 'at least' indicate when forming an inequality?

Back

'At least' indicates a minimum value and is represented by the '≥' symbol in an inequality.

Front

What is the significance of the constant term in an inequality?

Back

The constant term represents a fixed value that can affect the solution set of the inequality, determining the range of possible values for the variable.

Front

How do you interpret the solution of an inequality in a real-world context?

Back

The solution of an inequality represents a range of values that satisfy the conditions of the problem, which can be interpreted in terms of quantities, limits, or constraints in a real-world scenario.

Front

What is the relationship between inequalities and graphing on a number line?

Back

Inequalities can be represented on a number line, where open circles indicate 'greater than' or 'less than' and closed circles indicate 'greater than or equal to' or 'less than or equal to'.