Question

combining like terms
combine like terms to write an equivalent expression.
then use y = 5 to prove the expressions are equivalent.
1 + y + y + y + 1
complete the statements.
the equivalent expression is
the value of both expressions when y = 5 is
the expressions are

Explanation:

Step1: Combine like terms

The expression is \(1 + y + y + y + 1\). Combine the constant terms (\(1\) and \(1\)) and the \(y\) terms (\(y, y, y\)).
Constants: \(1 + 1 = 2\)
\(y\) terms: \(y + y + y = 3y\)
So the equivalent expression is \(3y + 2\).

Step2: Substitute \(y = 5\) into original expression

Original expression: \(1 + 5 + 5 + 5 + 1\)
Calculate step by step: \(1 + 5 = 6\), \(6 + 5 = 11\), \(11 + 5 = 16\), \(16 + 1 = 17\)

Step3: Substitute \(y = 5\) into equivalent expression

Equivalent expression: \(3(5) + 2\)
Calculate: \(3\times5 = 15\), \(15 + 2 = 17\)

Step4: Compare the values

Both expressions equal \(17\) when \(y = 5\), so they are equivalent.

Answer:

• The equivalent expression is \(3y + 2\).
• The value of both expressions when \(y = 5\) is \(17\).
• The expressions are equivalent.