To solve the equation
[tex]\[
4y \left[ 12 \div 4(5 - 9) \div \frac{1}{8} \right] + 7 = 55
\][/tex]
we follow these steps:
1. Simplify inside the parentheses first.
[tex]\[
5 - 9 = -4
\][/tex]
2. Next, perform the multiplication inside the brackets.
[tex]\[
4 \cdot (-4) = -16
\][/tex]
3. Now, substitute this back into the original bracket:
[tex]\[
12 \div (-16)
\][/tex]
4. Simplify the division:
[tex]\[
12 \div (-16) = -0.75
\][/tex]
5. The expression now is:
[tex]\[
-0.75 \div \frac{1}{8}
\][/tex]
6. Simplify the division by multiplying by the reciprocal:
[tex]\[
-0.75 \times 8 = -6
\][/tex]
7. Substitute this back into the original equation:
[tex]\[
4y \cdot (-6) + 7 = 55
\][/tex]
8. Simplify the multiplication:
[tex]\[
-24y + 7 = 55
\][/tex]
9. Isolate the term involving [tex]\( y \)[/tex]:
[tex]\[
-24y = 55 - 7 = 48
\][/tex]
10. Finally, solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{48}{-24} = -2
\][/tex]
The value of [tex]\( y \)[/tex] is:
[tex]\[
-2
\][/tex]
