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?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

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

Back

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

Front

When graphing the inequality b < 6, what type of circle is used?

Back

An open circle is used when graphing b < 6.

Front

What is the first step in solving the inequality 8x ≥ -32?

Back

Divide both sides by 8 to isolate x: x ≥ -4.

Front

How do you write an inequality for a maximum speed limit of 55?

Back

The inequality is s ≤ 55, where s is the speed.

Front

What is the cost structure of a taxi ride if it costs $1.75 plus $0.75 for each additional mile?

Back

The total cost can be represented as 1.75 + 0.75m, where m is the number of additional miles.

Front

If you have $20 to spend on a taxi ride, how do you set up the inequality?

Back

The inequality is 0.75m + 1.75 ≤ 20.