Multi-Step Inequalities

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 solve the inequality 6x + 2 + 6x < 14?

Back

Combine like terms to get 12x + 2 < 14, then subtract 2 from both sides to get 12x < 12, and finally divide by 12 to find x < 1.

Front

What does the inequality -4x + 14 ≤ 54 represent?

Back

This inequality represents a condition where the expression on the left is less than or equal to 54, which can be solved to find the range of values for x.

Front

How do you graph the solution set of the inequality -4a ≤ -28?

Back

First, solve for a to get a ≥ 7. Then, graph a number line, marking 7 with a closed circle and shading to the right to indicate all values greater than or equal to 7.

Front

What is the solution to the inequality a > 6?

Back

The solution indicates that a can take any value greater than 6, which can be represented graphically on a number line.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (e.g., <, >) do not include the boundary point, while non-strict inequalities (e.g., ≤, ≥) include the boundary point.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable, perform inverse operations (addition, subtraction, multiplication, division) on both sides of the inequality, keeping in mind to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What does the solution s > -12 mean?

Back

The solution indicates that s can take any value greater than -12, which can be represented graphically on a number line.

Front

What is the first step in solving the inequality -4x + 14 ≤ 54?

Back

The first step is to isolate the term with x by subtracting 14 from both sides, resulting in -4x ≤ 40.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.