Solving for Multistep Inequalities

Front

What is a multistep inequality?

Back

A multistep 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 'more than' in an inequality?

Back

'More than' is represented by the symbol '>'.

Front

How do you represent 'at most' in an inequality?

Back

'At most' is represented by the symbol '≤'.

Front

What does the inequality m ≥ -5 mean?

Back

It means that the value of m is greater than or equal to -5.

Front

How do you solve the inequality 9 ≥ -2m + 2 - 3?

Back

First, simplify to 9 ≥ -2m - 1, then add 1 to both sides to get 10 ≥ -2m, and finally divide by -2 (remember to flip the inequality) to get m ≥ -5.

Front

What is the first step in solving the inequality 12x + 400 < 1200?

Back

Subtract 400 from both sides to isolate the term with x.

Front

What does the inequality k < 3 indicate about the value of k?

Back

It indicates that k can take any value less than 3.

Front

How do you write an inequality for a situation where one plan is more expensive than another?

Back

You compare the total costs of both plans using an inequality, such as 40 + 0.04x > 30 + 0.09x.

Front

What is the solution to the inequality 40 + 0.04x > 30 + 0.09x?

Back

First, simplify to 0.04x - 0.09x > 30 - 40, which gives -0.05x > -10. Dividing by -0.05 (and flipping the inequality) gives x < 200.

Front

What does it mean to isolate a variable in an inequality?

Back

Isolating a variable means to manipulate the inequality so that the variable is on one side and all other terms are on the other side.