# Solving One-Step Equations (Negative and Positive Solutions)

Directions: Use the digits 1 to 9, at most one time each, to create two equations: one where x has a positive value and one where x has a negative value.

### Hint

How does the value of the number being added to x affect the value of x?
How does the value of the sum affect the value of x?

There are many answers. To get a positive solution, the number being added to x should be less than the sum. To get a negative solution, the number being added to x should be greater than the sum.

Source: Robert Kaplinsky

## Solving One-Step Inequalities with Addition

Directions: Using the digits 0 to 9 at most one time each, place a digit …

1. Could you extend this by asking: ” Using the same digits, create an equation where x has a negative value. What do you notice?”

2. I love the critical thinking required in these questions, but this particular question isn’t a sixth grade Common Core standard. The standard, 6.EE.7, asks students to solve multiplication and addition equation with numbers that are all “nonnegative rational numbers”. Is there a way to align this question to the standard better while still preserving the DOK level? Students do not learn operations with negative numbers until the seventh grade.

3. X is positive:
1 x 3 + x = 2 x 6
3 + x = 12
x = 9
X is negative:
3 x 6 + x = 2 x 5
18 + x = 10
x = -8

• Interesting that you interpreted the two boxes next to each other as multiplication. I was thinking they are two digit numbers.

Some positive solutions are:
13 + x = 25
24 + x = 35

Some negative solutions are:
25 + x = 13
35 + x = 24

4. Is it possible to do this and have x equal the same number in both equations? That’s originally what I thought I needed to do! 🙂