Flashcard - Solving 1 Dimensional Inequalities

Front

What is a one-dimensional inequality?

Back

A one-dimensional inequality is a mathematical expression that shows the relationship between two expressions using inequality symbols (like <, >, ≤, or ≥) in one variable.

Front

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

Back

First, distribute the 3: -2x - 12x + 18 ≤ 116. Combine like terms: -14x + 18 ≤ 116. Then, isolate x: -14x ≤ 98, so x ≥ -7.

Front

What does the solution x < -4 represent on a number line?

Back

It represents all values to the left of -4, not including -4 itself.

Front

What is the first step to solve the equation 3(x-2)=2x+7?

Back

Use the distributive property to get rid of the parentheses: 3x - 6 = 2x + 7.

Front

What does the inequality x ≥ 29 mean?

Back

It means that x can take any value greater than or equal to 29.

Front

What is the solution set for the inequality x < 4?

Back

The solution set includes all real numbers less than 4.

Front

How do you graph the inequality x ≤ 4 on a number line?

Back

Draw a solid dot on 4 and shade to the left to indicate all numbers less than or equal to 4.

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

What is the solution to the inequality 3x - 5 > 1?

Back

Add 5 to both sides: 3x > 6. Then divide by 3: x > 2.

Front

How do you solve the compound inequality -3 < 2x + 1 < 5?

Back

First, split it into two inequalities: -3 < 2x + 1 and 2x + 1 < 5. Solve each separately to find -2 < x < 2.