ItNotJesus
Answered

Solve for [tex]$y$[/tex]:

[tex]|6y + 3| + 8 = 35[/tex]

A. [tex]y = -4[/tex]

B. [tex]y = 4[/tex]

C. [tex]y = 4[/tex] or [tex]y = -\frac{23}{3}[/tex]

D. [tex]y = 4[/tex] or [tex]y = -5[/tex]



Answer :

GinnyAnswer
To solve the equation [tex]\( |6y + 3| + 8 = 35 \)[/tex], follow these steps:

1. Isolate the absolute value:
[tex]\[ |6y + 3| + 8 = 35 \][/tex]
Subtract 8 from both sides:
[tex]\[ |6y + 3| = 35 - 8 \][/tex]
Simplify:
[tex]\[ |6y + 3| = 27 \][/tex]

2. Set up the two cases for the absolute value:

The expression inside the absolute value can be either 27 or -27. Therefore, we have two cases:

Case 1:
[tex]\[ 6y + 3 = 27 \][/tex]

Case 2:
[tex]\[ 6y + 3 = -27 \][/tex]

3. Solve for [tex]\( y \)[/tex] in each case:

Case 1:
[tex]\[ 6y + 3 = 27 \][/tex]
Subtract 3 from both sides:
[tex]\[ 6y = 24 \][/tex]
Divide by 6:
[tex]\[ y = \frac{24}{6} \][/tex]
Simplify:
[tex]\[ y = 4 \][/tex]

Case 2:
[tex]\[ 6y + 3 = -27 \][/tex]
Subtract 3 from both sides:
[tex]\[ 6y = -30 \][/tex]
Divide by 6:
[tex]\[ y = \frac{-30}{6} \][/tex]
Simplify:
[tex]\[ y = -5 \][/tex]

4. State the solutions:

The solutions to the equation [tex]\( |6y + 3| + 8 = 35 \)[/tex] are:
[tex]\[ y = 4 \quad \text{or} \quad y = -5 \][/tex]

So, the correct answer is [tex]\( y = 4 \)[/tex] or [tex]\( y = -5 \)[/tex].

Other Questions