Final answer:
The number that makes both equations true is 2, as we simplify the given equations to find that x = 2 in both cases.
Step-by-step explanation:
The student is seeking to find the number that satisfies both given equations. To solve this, we should first simplify and examine each equation individually. The equations presented are:
- (5 x 2) × 3 = 5 x (x 3)
- (3x) x 4 = 3 × (2 x 4)
The goal is to find a common value of x that would make both equations true when substituted for x.
The first equation simplifies to 10 × 3 = 5x × 3, which implies that 5x = 10. This simplifies further to x = 2. For the second equation, (3x) × 4 = 3 × 8, we can simplify to 12x = 24, which gives us x = 2 once more. Therefore, the number 2 makes both equations true.
The equality of mathematical equations and the properties of multiplication are fundamental concepts used to solve problems like these.