-2 - 2x > -8
Understand the Problem
The question is asking to solve the inequality -2 - 2x > -8. This involves isolating x and determining the range of values that satisfy this inequality.
Answer
The solution is \( x < 3 \).
Answer for screen readers
The solution to the inequality is ( x < 3 ).
Steps to Solve
- Add 2 to both sides
To begin solving the inequality, we can add 2 to both sides to isolate the term involving (x):
$$ -2 - 2x + 2 > -8 + 2 $$
This simplifies to:
$$ -2x > -6 $$
- Divide by -2
Next, we divide both sides by -2. Remember, when dividing or multiplying both sides of an inequality by a negative number, we must flip the inequality sign:
$$ \frac{-2x}{-2} < \frac{-6}{-2} $$
This results in:
$$ x < 3 $$
- Interpret the solution
The solution indicates that (x) can take any value less than 3. This can be represented on a number line, with an open circle at 3 indicating that 3 is not included in the solution set.
The solution to the inequality is ( x < 3 ).
More Information
This inequality solution means that any number less than 3 will satisfy the original inequality ( -2 - 2x > -8 ). This type of problem is common in algebra and helps in understanding how to manipulate inequalities.
Tips
- Forgetting to flip the inequality sign when dividing by a negative number. Always remember that this is a key step when handling inequalities.
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