To solve the equation [tex]\( |5y - 10| = 5 \)[/tex], follow these steps:
### Step 1: Understand the Absolute Value Equation
The absolute value equation [tex]\( |5y - 10| = 5 \)[/tex] means that the expression inside the absolute value, [tex]\( 5y - 10 \)[/tex], can be either 5 or -5. Therefore, we set up two separate equations to solve for [tex]\( y \)[/tex].
### Step 2: Set Up the Two Equations
1. Equation 1: [tex]\( 5y - 10 = 5 \)[/tex]
2. Equation 2: [tex]\( 5y - 10 = -5 \)[/tex]
### Step 3: Solve Each Equation Separately
#### Solving Equation 1:
[tex]\[ 5y - 10 = 5 \][/tex]
1. Add [tex]\( 10 \)[/tex] to both sides:
[tex]\[ 5y - 10 + 10 = 5 + 10 \][/tex]
[tex]\[ 5y = 15 \][/tex]
2. Divide both sides by [tex]\( 5 \)[/tex]:
[tex]\[ y = \frac{15}{5} \][/tex]
[tex]\[ y = 3 \][/tex]
#### Solving Equation 2:
[tex]\[ 5y - 10 = -5 \][/tex]
1. Add [tex]\( 10 \)[/tex] to both sides:
[tex]\[ 5y - 10 + 10 = -5 + 10 \][/tex]
[tex]\[ 5y = 5 \][/tex]
2. Divide both sides by [tex]\( 5 \)[/tex]:
[tex]\[ y = \frac{5}{5} \][/tex]
[tex]\[ y = 1 \][/tex]
### Step 4: Combine the Solutions
The solutions to the equation [tex]\( |5y - 10| = 5 \)[/tex] are [tex]\( y = 3 \)[/tex] and [tex]\( y = 1 \)[/tex].
Thus, [tex]\( y \)[/tex] can be [tex]\( \boxed{3} \)[/tex] or [tex]\( \boxed{1} \)[/tex].
