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Solve for e. {:[7(2e-1)-3=6+6e],[e=◻]:}

Solve for e e .\newline7(2e−1)−3=6+6ee=□ \begin{array}{l} 7(2 e-1)-3=6+6 e \\ e=\square \end{array}

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Full solution

Q. Solve for e e .\newline7(2e−1)−3=6+6ee=□ \begin{array}{l} 7(2 e-1)-3=6+6 e \\ e=\square \end{array}
  1. Simplify and Solve Equation: First, let's simplify and solve the first equation in the system: 7(2e−1)−3=6+6e7(2e-1)-3=6+6e. Distribute the 77 into the parentheses: 7×2e−7×1−3=6+6e7\times 2e - 7\times 1 - 3 = 6 + 6e. This simplifies to: 14e−7−3=6+6e14e - 7 - 3 = 6 + 6e.
  2. Combine Like Terms: Combine like terms on the left side of the equation: 14e−10=6+6e14e - 10 = 6 + 6e.
  3. Isolate the ee Term: Subtract 6e6e from both sides to get all the ee terms on one side: 14e−6e−10=614e - 6e - 10 = 6. This simplifies to: 8e−10=68e - 10 = 6.
  4. Check Second Equation: Add 1010 to both sides to isolate the ee term: 8e−10+10=6+108e - 10 + 10 = 6 + 10. This simplifies to: 8e=168e = 16.
  5. Fill in the Value: Divide both sides by 88 to solve for ee: 8e8=168\frac{8e}{8} = \frac{16}{8}. This simplifies to: e=2e = 2.
  6. Fill in the Value: Divide both sides by 88 to solve for ee: 8e8=168\frac{8e}{8} = \frac{16}{8}.\newlineThis simplifies to: e=2e = 2.Now, let's check the second equation in the system: e=□e = \square.\newlineSince we have found that e=2e = 2, we can fill in the box with the value of ee.

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