Reviewing Inequalities so far

Front

What does the inequality a ≥ 11 represent on a number line?

Back

It represents all values of 'a' that are greater than or equal to 11, including 11 itself.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

First, subtract 14 from both sides: -4x ≤ 40. Then, divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What is the solution to the inequality 7(x + 3) < 5x + 13?

Back

Distributing gives 7x + 21 < 5x + 13. Subtract 5x from both sides: 2x + 21 < 13. Then, subtract 21: 2x < -8. Finally, divide by 2: x < -4.

Front

How do you solve the inequality (x/2) - 9 > -18?

Back

Add 9 to both sides: (x/2) > -9. Then, multiply by 2: x > -18.

Front

What does the inequality 10 < 3x + 19 mean?

Back

It means that 3x + 19 must be greater than 10. To solve, subtract 19: 3x > -9, then divide by 3: x > -3.

Front

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

Back

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

Front

What is the graphical representation of the inequality x < 5?

Back

It is represented by a number line with an open circle at 5 and a line extending to the left.

Front

How do you graph the inequality a ≤ 11?

Back

Draw a number line, place a closed circle at 11, and shade to the left to indicate all values less than or equal to 11.

Front

What does it mean if an inequality has no solution?

Back

It means there are no values that satisfy the inequality, often occurring when the variable cancels out and results in a false statement.

Front

How do you check if a solution to an inequality is correct?

Back

Substitute the solution back into the original inequality to see if it makes the inequality true.