any value of r that makes the inequality r > -6 true will also make the inequality -r < 6 true, and vice versa. when we divide both sides of the inequality by -1, we get: r > -6
The inequality in the image is “-r < 6”. To solve for the values of r that make this inequality true, we can isolate r by dividing both sides by -1. However, it’s important to remember that when we divide or multiply an inequality by a negative number, we have to flip the direction of the inequality. So, when we divide both sides of the inequality by -1, we get:
r > -6
Therefore, any value of r that is greater than -6 will make the inequality true. As you can see, any number to the right of -6 on the number line will make the inequality true.
In addition to solving for the values of r that make the inequality true, the image also asks you to write an equivalent inequality in terms of r. An equivalent inequality is one that has the same solutions as the original inequality. In this case, an equivalent inequality would be:
r > -6
This is because any value of r that makes the inequality r > -6 true will also make the inequality -r < 6 true, and vice versa.