Complete the equation so that it has infinite solutions.

4x + 10 = __x + __

1 answer

To create an equation with infinite solutions, the two sides must be equivalent for all values of \( x \). This means we need to find constants that make the equation true regardless of the value of \( x \).

Starting with the left side of the equation:

\[ 4x + 10 \]

We can express the right side in a way that will ensure both sides are identical. Let's break it down:

Let \( a \) represent the coefficient of \( x \) on the right side, and \( b \) represent the constant.

We want the right side to also equal \( 4x + 10 \). Therefore, we can set:

  • The coefficient of \( x \) on the right side to be \( 4 \): \( a = 4 \)
  • The constant on the right side must match the constant on the left side: \( b = 10 \)

Thus, we can fill in the blanks with these values:

The completed equation is:

\[ 4x + 10 = 4x + 10 \]

This equation holds true for all \( x \), resulting in infinite solutions.