Solve $-12x \leq 72$ and then plot the solution set on the number line.
Understand the Problem
The question asks to solve the inequality $-12x \leq 72$ for $x$, and then represent the solution set on a number line.
Answer
$x \geq -6$
Answer for screen readers
$x \geq -6$
Steps to Solve
- Isolate $x$ by dividing both sides by -12
To isolate the variable $x$, we need to divide both sides of the inequality by $-12$.
$-12x \leq 72$ $\frac{-12x}{-12} \geq \frac{72}{-12}$
- Remember to flip the inequality
Since we divided by a negative number, we must reverse the inequality sign.
$x \geq -6$
- Graph the solution on the number line
The solution $x \geq -6$ means that $x$ can be any number greater than or equal to $-6$. On a number line, this is represented by a closed circle at $-6$ (to indicate that $-6$ is included in the solution) and an arrow extending to the right, indicating all numbers greater than $-6$.
$x \geq -6$
More Information
The solution to the inequality $-12x \leq 72$ is $x \geq -6$. This means any value of $x$ that is greater than or equal to $-6$ will satisfy the original inequality.
Tips
A common mistake is forgetting to flip the inequality sign when dividing (or multiplying) by a negative number. Another common mistake is using an open circle instead of a closed circle when the inequality includes "equal to".
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