Question

explain whether 15t - 4t is equivalent to 4t - 15t. support your answer by evaluating the expressions for t = 2.
the expression 15t - 4t is equivalent to 4t - 15t because the negative sign in 15t - 4t belongs to the term 2.

Explanation:

Step1: Simplify \(15t - 4t\)

Combine like terms: \(15t - 4t=(15 - 4)t = 11t\)

Step2: Simplify \(4t - 15t\)

Combine like terms: \(4t - 15t=(4 - 15)t=- 11t\)

Step3: Evaluate for \(t = 2\) (for \(15t - 4t\))

Substitute \(t = 2\) into \(15t - 4t\): \(15\times2-4\times2 = 30 - 8=22\)

Step4: Evaluate for \(t = 2\) (for \(4t - 15t\))

Substitute \(t = 2\) into \(4t - 15t\): \(4\times2-15\times2=8 - 30=-22\)
Since \(11t
eq - 11t\) (except when \(t = 0\)) and the values at \(t = 2\) are \(22\) and \(-22\) (not equal), \(15t - 4t\) is not equivalent to \(4t - 15t\). The negative sign in \(15t-4t\) belongs to the term \(4t\), but the key is the sign of the resulting coefficient (or the value when evaluated) shows they are not equivalent.

Answer:

The expression \(15t - 4t\) is not equivalent to \(4t - 15t\). When \(t = 2\), \(15t-4t=15\times2 - 4\times2=30 - 8 = 22\) and \(4t - 15t=4\times2-15\times2=8 - 30=-22\). Since \(22
eq - 22\), the two expressions are not equivalent.