How do you solve In (x - 4) < 6?

Add 4 to both sides.

An inequality is treated just like an equation, except the carat (<) is reversed when multiplying by a negative number.

Add 4 to both sides

x-4+4<6+4

x<10

huh? Does no one see that "ln" there?

ln(x-4) < 6
since e^x is increasing, a<b ==> e^a < e^b
x-4 < e^6
x < 4+e^6

To solve the inequality In (x - 4) < 6, we need to isolate the variable x.

Step 1: Start by simplifying the left side of the inequality. Since In (x - 4) represents the natural logarithm of (x - 4), we can rewrite the inequality as log_e(x - 4) < 6. Here, log_e represents the natural logarithm.

Step 2: Rewrite the inequality using exponential form. In the exponential form of logarithms, we have e raised to the power of the logarithm equals the argument. Therefore, we get e^6 > x - 4.

Step 3: Add 4 to both sides of the inequality to isolate x. This gives us e^6 + 4 > x.

So, the solution to the inequality In (x - 4) < 6 is x > e^6 + 4.