To determine which expressions are equivalent to [tex]\(10j + 8k\)[/tex], let us analyze each given expression step by step:
1. Expression: [tex]\(10j + 8k\)[/tex]
- This expression matches exactly with the target expression [tex]\(10j + 8k\)[/tex]. Therefore, it is equivalent to [tex]\(10j + 8k\)[/tex].
2. Expression: [tex]\(5j + 3k\)[/tex]
- This expression is not equivalent to the target because the coefficients of [tex]\(j\)[/tex] and [tex]\(k\)[/tex] do not match those in [tex]\(10j + 8k\)[/tex]. Here, [tex]\(j\)[/tex] and [tex]\(k\)[/tex] have coefficients 5 and 3, respectively, instead of 10 and 8.
3. Expression: [tex]\(2(5j + 4k)\)[/tex]
- Let's simplify this expression:
[tex]\[
2(5j + 4k) = 2 \cdot 5j + 2 \cdot 4k = 10j + 8k
\][/tex]
- This simplifies exactly to [tex]\(10j + 8k\)[/tex]. Therefore, this expression is equivalent to [tex]\(10j + 8k\)[/tex].
4. Expression: [tex]\(4(j + 2k) + 6j\)[/tex]
- Let's simplify this one:
[tex]\[
4(j + 2k) + 6j = 4j + 8k + 6j = 4j + 6j + 8k = 10j + 8k
\][/tex]
- This also simplifies exactly to [tex]\(10j + 8k\)[/tex]. Therefore, this expression is equivalent to [tex]\(10j + 8k\)[/tex].
5. Expression: [tex]\(10j + 8k\)[/tex]
- This expression is an exact copy of the target expression [tex]\(10j + 8k\)[/tex]. Thus, it is obviously equivalent to [tex]\(10j + 8k\)[/tex].
Based on our analysis:
- Expression 1: Equivalent ([tex]\(10j + 8k\)[/tex])
- Expression 2: Not equivalent ([tex]\(5j + 3k\)[/tex])
- Expression 3: Equivalent ([tex]\(2(5j + 4k)\)[/tex])
- Expression 4: Equivalent ([tex]\(4(j + 2k) + 6j\)[/tex])
- Expression 5: Equivalent ([tex]\(10j + 8k\)[/tex])
Thus, the expressions that are equivalent to [tex]\(10j + 8k\)[/tex] are expressions 1, 3, and 4. The selected expressions are:
[1, 3, 4]
