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Answer: [tex]\textsf{y = 4/11}[/tex]
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Given: [tex]\textsf{2y + 14 = 6(4y + 1)}[/tex]
Find: [tex]\textsf{Solve for y}[/tex]
Solution: In order to solve for y we need to distribute the ride side of the expression, simplify, subtract 14 from both sides, subtract 24y from both sides, and divide both sides by -22.
Distribute and simplify
- [tex]\textsf{2y + 14 = (6 * 4y) + (6 * 1)}[/tex]
- [tex]\textsf{2y + 14 = 24y + 6}[/tex]
Subtract 14 from both sides
- [tex]\textsf{2y + 14 - 14 = 24y + 6 - 14}[/tex]
- [tex]\textsf{2y = 24y + 6 - 14}[/tex]
- [tex]\textsf{2y = 24y - 8}[/tex]
Subtract 24y from both sides
- [tex]\textsf{2y - 24y = 24y - 24y - 8}[/tex]
- [tex]\textsf{2y - 24y = -8}[/tex]
- [tex]\textsf{-22y = -8}[/tex]
Divide both sides by -22
- [tex]\textsf{-22y/-22 = -8/-22}[/tex]
- [tex]\textsf{y = -8/-22}[/tex]
- [tex]\textsf{y = 8/22}[/tex]
- [tex]\textsf{y = 4/11}[/tex]
Therefore, the expression simplifies down to y = 4/11.
