Let's solve the given equation step-by-step to determine which of the following equations is equivalent to [tex]\(4[x + 2(3x - 7)] = 22x - 65\)[/tex].
1. Start with the original equation:
[tex]\[
4[x + 2(3x - 7)] = 22x - 65
\][/tex]
2. Simplify inside the parentheses:
[tex]\[
2(3x - 7) = 6x - 14
\][/tex]
3. Substitute this simplification back into the equation:
[tex]\[
4[x + 6x - 14] = 22x - 65
\][/tex]
4. Combine like terms inside the square brackets:
[tex]\[
x + 6x - 14 = 7x - 14
\][/tex]
5. The equation now becomes:
[tex]\[
4[7x - 14] = 22x - 65
\][/tex]
6. Distribute the 4:
[tex]\[
4 \cdot 7x - 4 \cdot 14 = 28x - 56
\][/tex]
7. So, the simplified form of the equation is:
[tex]\[
28x - 56 = 22x - 65
\][/tex]
Therefore, the equivalent equation to [tex]\(4[x+2(3x-7)]=22x-65\)[/tex] is:
[tex]\[
28x - 56 = 22x - 65
\][/tex]
So, the correct answer is [tex]\(28x - 56 = 22x - 65\)[/tex].
