Solving One Variable and Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality by performing inverse operations, similar to solving an equation, while reversing the inequality sign if you multiply or divide by a negative number.

Front

What does the solution x > 5 represent on a number line?

Back

It represents all the points to the right of 5, not including 5 itself.

Front

What does the solution x < 2 represent on a number line?

Back

It represents all the points to the left of 2, not including 2 itself.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to.

Front

What is the graphical representation of y ≤ 2/5x + 1?

Back

It is a shaded region below the line y = 2/5x + 1, including the line itself.

Front

How do you graph the inequality y > -4x - 1?

Back

Graph the line y = -4x - 1 as a dashed line and shade the region above the line.

Front

What does the solution y < -4x - 1 indicate?

Back

It indicates that the values of y are less than the values given by the line y = -4x - 1.

Front

What is the solution set for the inequality 3x - 5 < 4?

Back

The solution set is x < 3.

Front

How do 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.