To determine if [tex]\( y = 53 \)[/tex] is a solution of the equation [tex]\( 6y + 10 = 12y \)[/tex], we will substitute [tex]\( y = 53 \)[/tex] into the equation and verify if both sides are equal.
1. Substitute [tex]\( y = 53 \)[/tex] into the left side of the equation [tex]\( 6y + 10 \)[/tex]:
[tex]\[
6 \cdot 53 + 10
\][/tex]
First, calculate [tex]\( 6 \cdot 53 \)[/tex]:
[tex]\[
6 \cdot 53 = 318
\][/tex]
Next, add 10:
[tex]\[
318 + 10 = 328
\][/tex]
So, the left side of the equation, when [tex]\( y = 53 \)[/tex], is 328.
2. Substitute [tex]\( y = 53 \)[/tex] into the right side of the equation [tex]\( 12y \)[/tex]:
[tex]\[
12 \cdot 53
\][/tex]
Calculate [tex]\( 12 \cdot 53 \)[/tex]:
[tex]\[
12 \cdot 53 = 636
\][/tex]
So, the right side of the equation, when [tex]\( y = 53 \)[/tex], is 636.
3. Compare both sides of the equation:
[tex]\[
328 \text{ (left side)} \neq 636 \text{ (right side)}
\][/tex]
Since 328 is not equal to 636, the equation [tex]\( 6y + 10 = 12y \)[/tex] does not hold true when [tex]\( y = 53 \)[/tex].
Therefore, [tex]\( y = 53 \)[/tex] is not a solution to the equation [tex]\( 6y + 10 = 12y \)[/tex].
