Solve for [tex]y[/tex] if

[tex]
4y \left[ \frac{12}{4(5-9)} \div \frac{1}{8} \right] + 7 = 55
[/tex]

Only enter the value, not the variable for your answer.



Answer :

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]