Question

Explain why an inequality such as \(3 a+6 \geq 0\) is called a multi-step inequality. Give another example of a multi-step inequality.

Short answer

A multi-step inequality refers to an inequality which requires more than one operation for solving it. The presented inequality \(3a + 6 \geq 0\) is a multi-step inequality as two steps are used to isolate 'a': subtraction and division. Another example can be \(2b - 4 < 8\) which also requires addition and division to isolate the variable 'b'.

Step-by-step solution

Understanding Multi-step Inequality

Consider the inequality given: \(3a + 6 \geq 0\). Here, to find the value of 'a', we need to perform at least two operations. Firstly, subtract '6' from both sides. Secondly, divide the result by '3'. These multiple steps make it a multi-step inequality.

Solving the Given Inequality

Start with the given inequality, \(3a + 6 \geq 0\). Subtract '6' from both sides, this gives: \[3a \geq -6\]. Now, divide both sides by '3' to isolate 'a'. This gives: \(a \geq -2\).

Providing Another Example

Consider another inequality: \(2b - 4 < 8\). Similar to the previous inequality, we would first perform addition of '4' to both sides: \(2b < 12\). Then, apply division by '2' to isolate 'b': \(b < 6\). This highlights that more than one operation is required to solve such inequalities, thus, qualifying it as a multi-step inequality.