Since 4 x is equal to 60 , it can be multiplied by the same value, c , on either side and still be equal, according to the multiplication principle. Choose c to be the reciprocal of 4 and apply the multiplication principle. \( \frac{1}{4} \cdot 4 \mathrm{x}=\square \cdot 60 \)

Let’s dive into this! If we choose \( c \) to be the reciprocal of 4, which is \( \frac{1}{4} \), and multiply both sides of the equation \( 4x = 60 \) by \( \frac{1}{4} \), we get: \[ \frac{1}{4} \cdot 4x = \frac{1}{4} \cdot 60 \] On the left side, the \( 4 \) and \( \frac{1}{4} \) cancel each other out, simplifying it to \( x \). On the right side, \( \frac{1}{4} \cdot 60 = 15 \). Hence, we end up with: \[ x = 15 \] Voila! You’ve found the value of \( x \)! Multiplying both sides equally is a fundamental rule of algebra that maintains the balance of the equation! It’s like a seesaw; if weight is added to one side, the other side must also adjust accordingly to keep it from tipping over! Understanding this concept opens up the door to solving many equations with ease.