For the inequality 5(x + 3) ≥ 9, what is the solution for x?
Understand the Problem
The question is asking us to solve the inequality $5(x + 3) \geq 9$ for the variable $x$ and determine the appropriate solution set from the provided options.
Answer
$x \geq -\frac{6}{5}$
Answer for screen readers
The solution to the inequality is:
$$ x \geq -\frac{6}{5} $$
Steps to Solve
- Distribute the 5
To solve the inequality, we need to distribute the 5 on the left side:
$$ 5(x + 3) \geq 9 $$
This gives us:
$$ 5x + 15 \geq 9 $$
- Isolate the variable term
Next, we isolate the term with the variable $x$ by subtracting 15 from both sides:
$$ 5x + 15 - 15 \geq 9 - 15 $$
This simplifies to:
$$ 5x \geq -6 $$
- Divide by 5
Now, we divide both sides by 5 to solve for $x$:
$$ \frac{5x}{5} \geq \frac{-6}{5} $$
This simplifies to:
$$ x \geq -\frac{6}{5} $$
- Express the solution set
The solution set can be expressed in interval notation. Since $x$ can be greater than or equal to $-\frac{6}{5}$, we write:
$$ x \in \left[-\frac{6}{5}, \infty\right) $$
The solution to the inequality is:
$$ x \geq -\frac{6}{5} $$
More Information
The solution $x \geq -\frac{6}{5}$ means that $x$ can be any value greater than or equal to $-\frac{6}{5}$. In interval notation, this is expressed as $[-\frac{6}{5}, \infty)$, indicating all values starting from $-\frac{6}{5}$ and extending infinitely towards positive infinity.
Tips
- Forgetting to switch the inequality sign when multiplying or dividing by a negative number. In this particular problem, no such operation occurs, but it's good to remember for future inequalities.
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