Two-Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 6t + 4 ≤ -2?

Back

Subtract 4 from both sides to get 6t ≤ -6, then divide by 6 to find t ≤ -1.

Front

What is the first step in solving the inequality 5x - 7 ≥ 8?

Back

Add 7 to both sides to isolate the term with the variable, resulting in 5x ≥ 15.

Front

What is the solution to the inequality 7k - 2 ≥ -9?

Back

Add 2 to both sides to get 7k ≥ -7, then divide by 7 to find k ≥ -1.

Front

How do you graph the solution of the inequality x ≥ -10?

Back

Draw a number line, place a closed circle on -10, and shade to the right to indicate all numbers greater than or equal to -10.

Front

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

Back

It represents a range of values for x that satisfy the condition that -4 times x plus 14 is less than or equal to 54.

Front

How do you isolate the variable in the inequality 7n - 1 > 76?

Back

Add 1 to both sides to get 7n > 77, then divide by 7 to find n > 11.

Front

What is the significance of the direction of the inequality sign when solving inequalities?

Back

The direction of the inequality sign indicates the relationship between the two sides; if you multiply or divide by a negative number, you must reverse the inequality sign.

Front

What is the solution set for the inequality 5x - 7 ≥ 8?

Back

The solution set is x ≥ 3, meaning all values of x that are greater than or equal to 3.

Front

What is the graphical representation of the inequality 7k - 2 ≥ -9?

Back

The graph will show a closed circle at -1 on the number line, with shading to the right to indicate all values greater than or equal to -1.