\( (x+1) \) is increased by \( 20 \% \) It is now the same as \( (x+6) \). Work out the value of \( x \).

To solve the equation, we first express \( (x + 1) \) increased by \( 20\% \). This can be written as: \[ 1.2(x + 1) = x + 6 \] Now, let's distribute \( 1.2 \): \[ 1.2x + 1.2 = x + 6 \] Next, we need to isolate \( x \). We can do this by moving \( x \) to the left side and constants to the right side: \[ 1.2x - x = 6 - 1.2 \] This simplifies to: \[ 0.2x = 4.8 \] To find \( x \), we divide both sides by \( 0.2 \): \[ x = \frac{4.8}{0.2} = 24 \] Thus, the value of \( x \) is \( 24 \).