Question

Complete the equation to create an equation with Infinitely Many Solutions. 5(3x - 4) = 4 + Choose...x + Choose...

Answer 1

To create an equation with infinitely many solutions, the left-hand side must be equal to the right-hand side for all values of \(x\). This can be done by ensuring that both sides simplify to the same expression.

Start with the left-hand side:

\[5(3x - 4) = 15x - 20\]

Now, let's write the right-hand side as:

\[4 + Ax + B\]

We want the equation to be true for all \(x\), meaning the coefficients of \(x\) and the constant terms must match on both sides.

From the left side, we have:

- Coefficient of \(x\) is \(15\).
- Constant term is \(-20\).

For the right side \(4 + Ax + B\), we have:

- Coefficient of \(x\) is \(A\).
- The constant term is \(4 + B\).

To create an equation with infinitely many solutions, set the coefficients equal:

1. \(A = 15\)
2. \(4 + B = -20\)

From the second equation, you can solve for \(B\):

\[B = -20 - 4\]
\[B = -24\]

Thus, we can choose \(A = 15\) and \(B = -24\).

Putting it all together, we have:

\[5(3x - 4) = 4 + 15x - 24\]

So the completed equation is:

\[5(3x - 4) = 4 + 15x - 24\]

This creates an equation that reduces to the same expression on both sides, thereby ensuring it has infinitely many solutions.