Answer:
4(x + 3) + 2x and 6(x + 2) are equivalent
Step-by-step explanation:
The best prove why two expressions must be equivalent is,
1. Simplify each expression to its simplest form
2. Show that the simplest form of them are equal
Let us do that with the given expressions
∵ The 1st expression is 4(x + 3) + 2x
→ At first, multiply the bracket (x + 3) by 4
∵ 4(x + 3) = 4(x) + 4(3) = 4x + 12
∴ The 1st expression = 4x + 12 + 2x
→ Add the like terms
∴ 4x + 12 + 2x = (4x + 2x) + 12 = 6x + 12
∴ The 1st expression = 6x + 12
∴ The simplest form of the 1st expression is 6x + 12
∵ The 2nd expression is 6(x + 2)
→ Multiply the bracket (x + 2) by 6
∵ 6(x + 2) = 6(x) + 6(2) = 6x + 12
∴ The 2nd expression = 6x + 12
∴ The simplest form of the 2nd expression is 6x + 12
∵ 6x + 12 = 6x + 12
∴ The simplest form of the two expressions are equal
∴ The expressions are equivalent
∴ 4(x + 3) + 2x and 6(x + 2) are equivalent
