Inequalities Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≤' mean?

Back

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

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you graph the inequality y ≤ -¾x - 1?

Back

To graph y ≤ -¾x - 1, draw the line y = -¾x - 1 as a solid line and shade below it.

Front

What is the solution to the inequality -8x < 48?

Back

The solution is x > -6.

Front

How do you solve the inequality 5x + y ≤ -1 for y?

Back

Rearranging gives y ≤ -5x - 1.

Front

What is the difference between 'x < -1' and 'x ≤ -1'?

Back

'x < -1' means x is less than -1 (not including -1), while 'x ≤ -1' means x is less than or equal to -1 (including -1).

Front

What does it mean if a graph shows x < -1?

Back

It means that all values of x to the left of -1 on the number line are solutions.

Front

How do you determine if a point (x, y) is a solution to the inequality y ≥ -3/4x + 3?

Back

Substitute the x-value into the inequality and check if the resulting y-value is greater than or equal to the calculated value.

Front

What is the graph of the inequality y < -3/4x + 3?

Back

The graph is a dashed line for y = -3/4x + 3, shading below the line.