To determine which of the given statements is equivalent to [tex]\(10x - 30\)[/tex], we will compare each expression to [tex]\(10x - 30\)[/tex] in detail.
1. Expression [tex]\(10(x - 20)\)[/tex]:
[tex]\[
10(x - 20) = 10x - 200
\][/tex]
Comparing this to [tex]\(10x - 30\)[/tex], we see:
[tex]\[
10x - 200 \neq 10x - 30
\][/tex]
Therefore, [tex]\(10(x - 20)\)[/tex] is not equivalent to [tex]\(10x - 30\)[/tex].
2. Expression [tex]\(10(x - 30)\)[/tex]:
[tex]\[
10(x - 30) = 10x - 300
\][/tex]
Comparing this to [tex]\(10x - 30\)[/tex], we see:
[tex]\[
10x - 300 \neq 10x - 30
\][/tex]
Therefore, [tex]\(10(x - 30)\)[/tex] is not equivalent to [tex]\(10x - 30\)[/tex].
3. Expression [tex]\(10(x - 3)\)[/tex]:
[tex]\[
10(x - 3) = 10x - 30
\][/tex]
Comparing this to [tex]\(10x - 30\)[/tex], we see:
[tex]\[
10x - 30 = 10x - 30
\][/tex]
Therefore, [tex]\(10(x - 3)\)[/tex] is indeed equivalent to [tex]\(10x - 30\)[/tex].
4. Expression [tex]\(10 + (x - 20)\)[/tex]:
[tex]\[
10 + (x - 20) = x - 10
\][/tex]
Comparing this to [tex]\(10x - 30\)[/tex], we see:
[tex]\[
x - 10 \neq 10x - 30
\][/tex]
Therefore, [tex]\(10 + (x - 20)\)[/tex] is not equivalent to [tex]\(10x - 30\)[/tex].
After comparing all the given expressions, the statement that is equivalent to [tex]\(10x - 30\)[/tex] is:
[tex]\[
\boxed{10(x - 3)}
\][/tex]
