To find the values of \( A \) and \( B \) that will result in the equation \( 8 + Ax = B + 5x \) having infinite solutions, the two sides of the equation must represent the same linear relationship. This means the coefficients of \( x \) and the constant terms must match.
We can rearrange the original equation:
\[ Ax - 5x = B - 8 \]
Factoring out \( x \) from the left-hand side gives:
\[ (A - 5)x = B - 8 \]
For this equation to hold true for any value of \( x \), both sides must be equal. This happens when:
- The coefficient of \( x \) on the left is 0: \( A - 5 = 0 \)
- The constant term on the right is also 0: \( B - 8 = 0 \)
From the first condition:
\[ A - 5 = 0 \implies A = 5 \]
From the second condition:
\[ B - 8 = 0 \implies B = 8 \]
Thus, the values are:
A = 5
B = 8
So you would enter:
A equals 5
B equals 8
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