Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≤' represent?

Back

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

Front

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

Back

To solve the inequality, first distribute: 3x - 9 ≤ 2x + 4. Then, isolate x: 3x - 2x ≤ 4 + 9, which simplifies to x ≤ 13.

Front

What is the solution set of the inequality 4x - 10 ≤ 22?

Back

To solve, add 10 to both sides: 4x ≤ 32. Then divide by 4: x ≤ 8.

Front

How do you interpret the solution x ≤ 8 in a real-world context?

Back

It means that any value of x that is 8 or less satisfies the inequality.

Front

What does the inequality 11 ≤ a imply about the variable a?

Back

It implies that a must be greater than or equal to 11.

Front

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

Back

First, distribute: -2x - 12x + 18 ≤ 116. Combine like terms: -14x + 18 ≤ 116. Then, isolate x: -14x ≤ 98, which simplifies to x ≥ -7.

Front

What is the graphical representation of the inequality x ≤ 8?

Back

The graph is a number line with a closed circle at 8 and a line extending to the left.

Front

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

Back

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

Front

How can you check if a value is a solution to an inequality?

Back

Substitute the value into the inequality and see if the statement is true.