Determine the number of solutions that exist to the equation below. $$ 8(j-4)=2(4 j-16) $$

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UpStudy AI · Accepted Answer

To determine the number of solutions to the equation:

$$
8(j - 4) = 2(4j - 16)
$$

Let's simplify both sides of the equation:

1. **Expand the Left Side:**
   $$
   8(j - 4) = 8j - 32
   $$

2. **Expand the Right Side:**
   $$
   2(4j - 16) = 8j - 32
   $$

Now, the equation becomes:
$$
8j - 32 = 8j - 32
$$

Subtract $$8j$$ from both sides:
$$
-32 = -32
$$

This simplifies to a true statement, regardless of the value of $$j$$. This means that **any real number** substituted for $$j$$ will satisfy the equation.

**Conclusion:**  
There are **infinitely many solutions** to the equation, as it holds true for all real numbers $$j$$.

**Answer:**  
There are infinitely many real numbers j that satisfy the equation.
There are infinitely many solutions for $$ j $$.

Determine the number of solutions that exist to the equation below. \[ 8(j-4)=2(4 j-16) \]

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