Question

Jeremy wants to determine the number of solutions for the equation below without actually solving the equation.

Negative 3 (x + 1) + 3 x = negative 3 (x minus 1) + 3

Answer 1

there is only one solution

Explanation:

Answer 2

1 solution

Explanation:

Jeremy can simplify the equation enough to determine if the x-coefficient on one side of the equation is the same or different from the x-coefficient on the other side. Here, that simplification is ...

-3x -3 +3x = -3x +3 +3

We see that the x-coefficient on the left is 0; on the right, it is -3. These values are different, so there is one solution.

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In the attached, the left-side expression is called y1; the right-side expression is called y2. The two expressions are equal where the lines they represent intersect. That point of intersection is x=3. (For that value of x, both sides of the equation have a value of -3.)

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Additional comment

If the equation's x-coefficients were the same, we'd have to look at the constants. If they're the same, there are an infinite number of solutions. If they are different, there are no solutions.