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

  1 solution

Step-by-step 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.

78.59 is the mean

step-by-step explanation: