NOV 25 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 combining like terms, distributing, and isolating the variable.

Front

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

Back

1. Distribute: 30 + 15r + 7 ≥ 127 2. Combine like terms: 15r + 37 ≥ 127 3. Subtract 37: 15r ≥ 90 4. Divide by 15: r ≥ 6.

Front

What does the solution r ≥ 6 represent in a real-world context?

Back

It means that the value of r must be 6 or greater, which could represent a minimum requirement in a scenario, such as a score needed to pass.

Front

What is the first step in solving the inequality 6x + 2 < 14?

Back

Subtract 2 from both sides: 6x < 12.

Front

How do you isolate x in the inequality 6x < 12?

Back

Divide both sides by 6: x < 2.

Front

What does the solution x < 1 indicate?

Back

It indicates that x can take any value less than 1, which can be used to determine acceptable values in a given situation.

Front

How do you solve the inequality 28 - k ≥ 7(k - 4)?

Back

1. Distribute: 28 - k ≥ 7k - 28 2. Add k to both sides: 28 ≥ 8k - 28 3. Add 28: 56 ≥ 8k 4. Divide by 8: 7 ≥ k or k ≤ 7.

Front

What is the significance of the inequality k ≤ 7?

Back

It means that k can be any value less than or equal to 7, which can be important in constraints or limits in problems.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

What does it mean to graph an inequality on a number line?

Back

Graphing an inequality on a number line involves shading the region that represents all possible solutions and using an open or closed circle to indicate whether endpoints are included.