Final answer:
The expressions (x + 10) + x + 9 and 2(x + 7) + 5 are both simplified to 2x + 19, therefore, they are equivalent. Simplification is done by combining like terms and distributing multiplication over addition.
Step-by-step explanation:
Are the Expressions Equivalent?
To determine whether the expressions (x + 10) + x + 9 and 2(x + 7) + 5 are equivalent, we will use the properties of operations to simplify and compare the two expressions.
For the first expression, we simply combine like terms:
- (x + 10) + x + 9 = x + x + 10 + 9
- = 2x + 19
For the second expression, we first distribute the 2, then combine like terms:
- 2(x + 7) + 5 = 2x + 14 + 5
- = 2x + 19
After simplification, we find that both expressions are indeed equivalent since they both simplify to 2x + 19.
We have applied the commutative property A+B=B+A which holds for the addition of numbers, as well as the distributive property when expanding the second expression. After eliminating terms where possible and simplifying, we check the answer to ensure it is reasonable. Both expressions reduce to the same form, confirming their equivalence.