Determine if (-1,-4) is a Solution x+y< =-3 , (-1,-4)

Solution:

Step 1:

Substitute $x=-1$ and $y=-4$ into the inequality $x+y\le -3$ to verify if the pair satisfies the condition. Compute $-1+(-4)\le -3$.

Step 2:

Perform the addition of $-1$ and $-4$. The result is $-5\le -3$.

Step 3:

Evaluate the inequality. Since $-5$ is less than or equal to $-3$, the inequality holds true.

Step 4:

The inequality being true indicates that the pair $(-1,-4)$ is indeed a solution to the inequality $x+y\le -3$.

Knowledge Notes:

To determine whether an ordered pair is a solution to an inequality, you must:

1. Substitution: Replace the variables in the inequality with the values from the ordered pair.

2. Perform Arithmetic: Carry out any necessary arithmetic operations to simplify the inequality.

3. Evaluate the Inequality: Check if the resulting statement is true or false.

4. Conclusion: If the inequality is true, the ordered pair is a solution. If it is false, the ordered pair is not a solution.

Inequalities are mathematical expressions involving the symbols $>$ (greater than), $<$ (less than), $\ge$ (greater than or equal to), and $\le$ (less than or equal to). They indicate the relationship between two values.

When dealing with inequalities, it is important to remember that multiplying or dividing both sides by a negative number reverses the inequality sign. However, this is not relevant for this particular problem since we are only substituting and evaluating without altering the inequality itself.