Question

which expressions are equivalent to $5(t - 2)$? select all that apply.
a $5t - 2$
b $5t - 10$
c $5t + 10$
d $5(t - 1) - 5$
e $5(t + 1) + 5$
f $4(t - 2) + t - 2$

Explanation:

Step1: Expand \(5(t - 2)\)

Using the distributive property \(a(b - c)=ab - ac\), we have \(5(t - 2)=5\times t-5\times2 = 5t - 10\).

Step2: Analyze Option D

Simplify \(5(t - 1)-5\). First, expand \(5(t - 1)\) to get \(5t-5\), then subtract 5: \(5t - 5-5=5t - 10\).

Step3: Analyze Option F

Simplify \(4(t - 2)+t - 2\). Expand \(4(t - 2)\) to get \(4t-8\), then add \(t - 2\): \(4t-8+t - 2=(4t + t)+(-8 - 2)=5t - 10\).

Step4: Analyze other options

• Option A: \(5t - 2

eq5t - 10\).

• Option C: \(5t + 10

eq5t - 10\).

• Option E: Expand \(5(t + 1)+5\) to get \(5t+5 + 5=5t + 10

eq5t - 10\).

Answer:

B. \(5t - 10\), D. \(5(t - 1)-5\), F. \(4(t - 2)+t - 2\)