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Problem 6

# Explain how to find the opposite of the number that is 2 units less than $$-17$$ on the number line. Justify your answer on the number line. cant copy graph

Expert verified
The opposite of the number that is 2 units less than $$-17$$ on the number line can be found by first identifying the number 2 units less than $$-17$$, which is $$-19$$. The opposite of this number is $$-(-19)$$, which equals $$19$$. The position of $$19$$ on the number line, at an equal distance from $$0$$ as $$-19$$ but on the opposite side, verifies that it is indeed the opposite of the number that is 2 units less than $$-17$$.
See the step by step solution

## Step 1: Find the number 2 units less than -17 on the number line.

To do this, we will move 2 units to the left on the number line from the point -17. Mathematically, this can be represented as: $-17 + (-2) = -19$. So, the number that is 2 units less than -17 on the number line is -19.

## Step 2: Find the opposite of -19 on the number line.

The opposite of any number 'x' on the number line is represented as '-x'. In this case, the opposite of -19 is -(-19), which is equal to 19. Therefore, the opposite of the number that is 2 units less than -17 on the number line is 19.

## Step 3: Justify the position of 19 on the number line.

Let's visualize the positions of -17, -19, and 19 on the number line. Since 19 is the opposite of -19, it is positioned at the same distance from 0 as -19, but on the opposite side. Remember that -17 is to the left of 0, -19 is further left of -17, and 19 is to the right of 0. The position of 19 on the number line verifies that it is indeed the opposite of -19. To conclude, the opposite of the number that is 2 units less than -17 on the number line is 19, as demonstrated by its position on the number line.

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