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

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

A. [tex]y = 5[/tex] or [tex]y = -\frac{20}{3}[/tex]
B. [tex]y = -5[/tex]
C. [tex]y = 5[/tex]
D. [tex]y = 5[/tex] or [tex]y = -4[/tex]

Sagot :

GinnyAnsweridn
To solve the equation:

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

First, isolate the absolute value expression by subtracting 8 from both sides:

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

[tex]\[ |6y - 3| = 27 \][/tex]

Now, we need to solve the absolute value equation. Recall that if [tex]\(|A| = B\)[/tex], then [tex]\(A = B\)[/tex] or [tex]\(A = -B\)[/tex]. Applying this property here:

[tex]\[ 6y - 3 = 27 \quad \text{or} \quad 6y - 3 = -27 \][/tex]

Let's solve each case separately.

### Case 1: [tex]\(6y - 3 = 27\)[/tex]

Add 3 to both sides:

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

[tex]\[ 6y = 30 \][/tex]

Divide by 6:

[tex]\[ y = \frac{30}{6} \][/tex]

[tex]\[ y = 5 \][/tex]

### Case 2: [tex]\(6y - 3 = -27\)[/tex]

Add 3 to both sides:

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

[tex]\[ 6y = -24 \][/tex]

Divide by 6:

[tex]\[ y = \frac{-24}{6} \][/tex]

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

Therefore, the solutions for the equation [tex]\(|6y - 3| + 8 = 35\)[/tex] are:

[tex]\[ y = 5 \quad \text{or} \quad y = -4 \][/tex]
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