Find the solution set of `x+10gt4x-5`.

Answer

To solve the inequality \( x + 10 > 4x - 5 \), we will follow these steps:

### Step 1: Rearranging the Inequality
We start with the inequality:
\[ x + 10 > 4x - 5 \]
To isolate \( x \), we can move all terms involving \( x \) to one side and constant terms to the other side. We can subtract \( x \) from both sides:
\[ 10 > 4x - x - 5 \]
This simplifies to:
\[ 10 > 3x - 5 \]

### Step 2: Isolating the Variable
Next, we add 5 to both sides to isolate the term with \( x \):
\[ 10 + 5 > 3x \]
This simplifies to:
\[ 15 > 3x \]
or equivalently:
\[ 3x < 15 \]

### Step 3: Dividing by the Coefficient of \( x \)
Now, we divide both sides by 3 to solve for \( x \):
\[ x < 5 \]

### Step 4: Writing the Solution Set
The solution \( x < 5 \) means that \( x \) can take any value less than 5. In interval notation, this is expressed as:
\[ (-\infty, 5) \]

### Final Answer
The solution set of the inequality \( x + 10 > 4x - 5 \) is:
\[ x \in (-\infty, 5) \]

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