Finish the equation so that the equation has infinite amount of solutions. Click Here for Rubric

8
(
7
x
+
5
)

8
=
8(7x+5)−8=

1 answer

To create an equation that has an infinite number of solutions, we can set both sides of the equation to be identical.

Starting with the expression you provided:

\[ 8(7x + 5) - 8 \]

Let's simplify the left-hand side:

  1. Distribute the 8: \[ 8(7x) + 8(5) - 8 = 56x + 40 - 8 = 56x + 32 \]

Now we'll set the right-hand side equal to the left-hand side:

\[ 56x + 32 = 56x + 32 \]

This equation is true for all values of \( x \), since both sides are identical. Thus, it has an infinite number of solutions.

Therefore, you can finish the equation like this:

\[ 8(7x + 5) - 8 = 56x + 32 \]

or simply:

\[ 8(7x + 5) - 8 = 8(7x + 5) - 8 \]

Both forms establish that the equation has infinite solutions.