Question

Katrice is solving the following linear equation. 3 + 1/3 * x - 10 = 2/3 * x - 2 - 4/3 * x Her final two steps are: 1/3 * x - 7 = - 2/3 * x - 2 x = 5 Which statement correctly interprets Katrice's solution? The solution is x = 5 There is no solutions The solution is the ordered pair 1,5 or There are infinitely many solutions since x is a whole number

Answer 1

Okay, let's break this down step-by-step:

Katrice's original equation:

3 + 1/3 * x - 10 = 2/3 * x - 2 - 4/3 * x

She combines like terms on the left side:

-7 = - 2/3 * x - 2

She adds 2 to both sides:

-5 = - 2/3 * x

She divides both sides by -2/3:

x = 5

So the correct interpretation of Katrice's solution is:

The solution is x = 5

The other options are incorrect:

There is no solutions - This is incorrect, there is a solution.

The solution is the ordered pair 1,5 - No, the solution is the scalar x = 5, not an ordered pair.

There are infinitely many solutions since x is a whole number - No, the solution is a unique scalar, x = 5.

So in summary, Katrice solved the linear equation by combining like terms, adding to both sides, and dividing both sides by -2/3 to isolate x. The solution is x = 5.