Solving 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 a monthly payment in an inequality when given a total budget?

Back

You can represent the monthly payment as a variable (e.g., x) and set up an inequality based on the total budget minus any initial payments.

Front

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

Back

The symbol '<' means 'less than' and indicates that the value on the left side is smaller than the value on the right side.

Front

How do you solve the inequality 12x + 400 < 1200 for x?

Back

First, subtract 400 from both sides to get 12x < 800, then divide both sides by 12 to find x < 66.67.

Front

What is the first step in solving the inequality a - 6 ≤ 15 + 8a?

Back

The first step is to isolate the variable a by moving all terms involving a to one side and constant terms to the other side.

Front

What does the solution a ≥ -3 indicate about the variable a?

Back

The solution a ≥ -3 indicates that a can be any value greater than or equal to -3.

Front

How do you solve the inequality 28 - k ≥ 7(k - 4)?

Back

First, distribute the 7 on the right side to get 28 - k ≥ 7k - 28, then combine like terms to isolate k.

Front

What is the solution to the inequality 4(5x + 2) ≤ 28?

Back

The solution is x ≤ 1, found by first distributing 4, simplifying, and then isolating x.

Front

What does the term 'infinite solutions' mean in the context of inequalities?

Back

Infinite solutions mean that there are countless values that satisfy the inequality, often occurring when the inequality simplifies to a true statement.

Front

How do you interpret the inequality -2(5 + 6n) < 6(8 - 2n)?

Back

You interpret it by first distributing both sides, then combining like terms to find the range of values for n.