Question

Complete the equation so it has infinitely many solutions. 4x + 7 = 4(x + 3) –

Answer 1

Answer:

4x + 7 = 4(x + 3) –    5  

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Answer 2

Answer:

The completed equation must be 4x + 7 = 4(x + 3) – 5

Step-by-step explanation:

For this equation to have infinitely many solutions, we must solve for x and reach a point where we have "0x = 0".

Notice that, x = ... -2, -1, 0, 1, 2 ... are all solutions of "0x = 0".

We will call the missing term "t", then the given equations is...

4x + 7 = 4(x + 3) – t

We distribute 4 over the parentheses on right side...

4x + 7 = 4x + 12 – t

We substract 7 on both sides...

4x + 7 - 7 = 4x + 12 – t - 7

4x = 4x + 5 – t

We substract 4x on both sides...

4x - 4x = 4x + 5 – t  - 4x

0x = 5 - t

As state above, this equation will have infinitely many solutions if the right side is 0...

5 - t = 0

5 = t