Tell whether (-8, -2/3) is a solution of y + 1 < -1/6(x + 6). It _____ a solution.
Understand the Problem
The question is asking whether the point (-8, -2/3) satisfies the inequality given by y + 1 < -1/6(x + 6). To determine this, we need to substitute x = -8 and y = -2/3 into the inequality and evaluate if it holds true.
Answer
It is not a solution.
Answer for screen readers
It is not a solution.
Steps to Solve
- Substituting Values into the Inequality
Substitute ( x = -8 ) and ( y = -\frac{2}{3} ) into the inequality ( y + 1 < -\frac{1}{6}(x + 6) ).
This gives:
$$ -\frac{2}{3} + 1 < -\frac{1}{6}(-8 + 6) $$
- Simplifying the Left Side
Calculate the left side of the inequality:
$$ -\frac{2}{3} + 1 = -\frac{2}{3} + \frac{3}{3} = \frac{1}{3} $$
- Simplifying the Right Side
Calculate the right side:
$$
- \frac{1}{6}(-2) = \frac{2}{6} = \frac{1}{3} $$
So the inequality becomes:
$$ \frac{1}{3} < \frac{1}{3} $$
- Evaluating the Inequality
The statement ( \frac{1}{3} < \frac{1}{3} ) is false; hence the point does not satisfy the inequality.
It is not a solution.
More Information
When checking if a point satisfies an inequality, comparing the left and right sides involves ensuring one side is strictly less than the other. Here, the equality indicates the point is on the line, but does not satisfy the strict inequality.
Tips
- Miscalculating the left or right side of the inequality.
- Forgetting to simplify fractions properly.
- Assuming equality in inequalities.
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