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

[tex]|4y - 2| + 7 = 37[/tex]

A. [tex]y = 8[/tex]

B. [tex]y = -8[/tex]

C. [tex]y = 8[/tex] or [tex]y = -\frac{21}{2}[/tex]

D. [tex]y = 8[/tex] or [tex]y = -7[/tex]

Sagot :

GinnyAnswer
To solve the equation

[tex]\[ |4y - 2| + 7 = 37, \][/tex]

let's proceed with the following steps:

1. Isolate the absolute value expression.

[tex]\[ |4y - 2| = 37 - 7 \][/tex]
[tex]\[ |4y - 2| = 30 \][/tex]

2. Remove the absolute value by considering both possible cases for \(4y - 2\):

[tex]\[ 4y - 2 = 30 \quad \text{or} \quad 4y - 2 = -30 \][/tex]

Let's solve each case separately:

### Case 1: \(4y - 2 = 30\)

Solve for \( y \):

[tex]\[ 4y - 2 = 30 \][/tex]

Add 2 to both sides:

[tex]\[ 4y = 32 \][/tex]

Divide both sides by 4:

[tex]\[ y = 8 \][/tex]

### Case 2: \(4y - 2 = -30\)

Solve for \( y \):

[tex]\[ 4y - 2 = -30 \][/tex]

Add 2 to both sides:

[tex]\[ 4y = -28 \][/tex]

Divide both sides by 4:

[tex]\[ y = -7 \][/tex]

So the solutions for the equation \(|4y - 2| + 7 = 37\) are:

[tex]\[ y = 8 \quad \text{or} \quad y = -7 \][/tex]

The correct answer is:

[tex]\[ y = 8 \quad \text{or} \quad y = -7 \][/tex]
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