Solving Multi-Step Inequalities with Word Problems

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

How do you represent an inequality on a number line?

Back

An inequality is represented on a number line using an open circle for < or > and a closed circle for ≤ or ≥.

Front

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

Back

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

Front

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

Back

'<'' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

How do you solve the inequality -2x + 3(-4x + 6) ≤ 116?

Back

First, distribute: -2x - 12x + 18 ≤ 116. Combine like terms: -14x + 18 ≤ 116. Then, isolate x: -14x ≤ 98, so x ≥ -7.

Front

What is the first step in solving the inequality 6 > x?

Back

The first step is to isolate x by rewriting the inequality as x < 6.

Front

In the context of a word problem, how do you set up an inequality for a budget?

Back

Identify the total amount available and set up an inequality where the total cost is less than or equal to the budget.

Front

What does the solution x ≥ -7 represent in a real-world context?

Back

It means that the variable x can take any value greater than or equal to -7, which may represent a minimum requirement or threshold.

Front

When solving the inequality -p - 4p > -10, what is the first step?

Back

Combine like terms: -5p > -10, then divide by -5, remembering to flip the inequality sign: p < 2.

Front

What is the significance of an open circle when graphing b < 6?

Back

An open circle indicates that 6 is not included in the solution set; values can approach 6 but cannot equal it.