Question
(1)) Complete the equation so it has infinitely many solutions.
Ask by Daniel Hill. in the United States
Mar 07,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The blank should be filled with 10 to make the equation have infinitely many solutions.
Solution
We start with the equation:
\[
25x + \square = 7 + 3 + 25x
\]
**Step 1: Simplify the Right Side**
Add the constant terms on the right:
\[
7 + 3 = 10,
\]
so the equation becomes:
\[
25x + \square = 10 + 25x.
\]
**Step 2: Determine the Value for the Blank**
For the equation to have infinitely many solutions, it must be true for every \( x \). This happens when both sides of the equation are identical. That means the constant term added to \( 25x \) on the left must equal the constant term on the right. Therefore, we set:
\[
\square = 10.
\]
**Step 3: Write the Final Equation**
Substitute \( 10 \) in place of \( \square \):
\[
25x + 10 = 10 + 25x.
\]
Since this equality holds for all \( x \), the equation indeed has infinitely many solutions.
**Final Answer:** The blank should be filled with \(10\).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To have infinitely many solutions, we want both sides of the equation to be equal for all values of
If you ever encounter an equation where both sides seem equal but includes different terms, remember that adding the same term to both sides can ensure that the equation remains balanced. This will help you manipulate equations creatively while retaining the same value. So, don’t shy away from using this method!
