Multistep inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, or division.

Front

How do you solve the inequality 5(6 + 3r) + 7 ≥ 127?

Back

First, distribute: 30 + 15r + 7 ≥ 127. Combine like terms: 15r + 37 ≥ 127. Subtract 37: 15r ≥ 90. Divide by 15: r ≥ 6.

Front

What does the solution r ≥ 6 mean in terms of a number line?

Back

It means that the solution includes all numbers greater than or equal to 6, represented by a closed dot at 6 and a line extending to the right.

Front

How do you write the inequality x < 8 in interval notation?

Back

In interval notation, x < 8 is written as (-∞, 8).

Front

What is the solution to the inequality -p - 4p > -10?

Back

Combine like terms: -5p > -10. Divide by -5 (remember to flip the inequality): p < 2.

Front

How do you solve the inequality -8(x - 3) - 4x < 108?

Back

Distribute: -8x + 24 - 4x < 108. Combine like terms: -12x + 24 < 108. Subtract 24: -12x < 84. Divide by -12 (flip the inequality): x > -7.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (e.g., < or >) does not include the endpoint, while a non-strict inequality (e.g., ≤ or ≥) includes the endpoint.

Front

What does the solution x ≤ -11 represent on a number line?

Back

It represents all numbers less than or equal to -11, shown with a closed dot at -11 and a line extending to the left.

Front

How do you check the solution of an inequality?

Back

Substitute a value from the solution set back into the original inequality to see if it holds true.

Front

What is the importance of flipping the inequality sign when multiplying or dividing by a negative number?

Back

Flipping the inequality sign ensures that the relationship between the two sides of the inequality remains valid.