Question

These two expression are equivalent when x = 3
2x+1 and 5−7x
True or False

Answer 1

The two expressions x = 32x + 1 and 5 - 7x are not equivalent when x = -1/31 and x = 5/7. Therefore, the statement is False.

Step-by-step explanation:

When two expressions are equivalent, it means that they have the same value when the same values are plugged in for the variables. To determine if the expressions x = 32x + 1 and 5 - 7x are equivalent, we need to solve for x and check if the solutions are the same for both expressions.

Let's solve the first expression, x = 32x + 1:

To do this, we'll subtract 32x from both sides of the equation:

x - 32x = 1

Combine like terms:

-31x = 1

Divide both sides by -31 to solve for x:

x = -1/31

Now let's solve the second expression, 5 - 7x:

We'll set the expression equal to 0 and solve for x:

5 - 7x = 0

Subtract 5 from both sides:

-7x = -5

Divide both sides by -7 to solve for x:

x = 5/7

Since the solutions for both expressions are different, the two expressions are NOT equivalent when x = -1/31 and x = 5/7. Therefore, the statement is False.