Question
Solve the equation, if possible. (If there is no solution; enter NO SOLUTION. If all real numbers are solutions, enter REALS.) \[ 45(b-1)+5=5(9 b-8) \] SUBMIT ANSWER
Ask by Patel Cruz. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
All real numbers are solutions.
Solution
1. Start with the equation:
\[
45(b-1)+5=5(9b-8)
\]
2. Expand the left side:
\[
45b - 45 + 5 = 45b - 40
\]
3. Expand the right side:
\[
5(9b-8) = 45b - 40
\]
4. The equation becomes:
\[
45b - 40 = 45b - 40
\]
5. Since both sides are identical, the equation holds true for all real values of \( b \).
REALS
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Simplify this solution The Deep Dive
To solve the equation \( 45(b-1)+5=5(9 b-8) \), we first expand both sides. Starting with the left-hand side: \[ 45(b-1) + 5 = 45b - 45 + 5 = 45b - 40 \] Now, for the right-hand side: \[ 5(9b - 8) = 45b - 40 \] Now we have the equation: \[ 45b - 40 = 45b - 40 \] Since both sides are equal, this equation holds true for any value of \( b \). Therefore, the solution to this equation is: \[ \text{REALS} \]
