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Solve the equation below and write your answer using set notation.

3（xー1）=10-2（2x+3）
・{x=1}
・{10 over 7}
・{1}
・no solution
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1 answer

To solve the equation \( 3(x - 1) = 10 - 2(2x + 3) \), we will start by simplifying both sides of the equation.

  1. Distribute on the left side: \[ 3(x - 1) = 3x - 3 \]

  2. Distribute on the right side: \[ 2(2x + 3) = 4x + 6 \] Therefore the right side becomes: \[ 10 - (4x + 6) = 10 - 4x - 6 = 4 - 4x \]

  3. Now rewrite the equation with the simplified sides: \[ 3x - 3 = 4 - 4x \]

  4. Add \( 4x \) to both sides: \[ 3x + 4x - 3 = 4 \] This simplifies to: \[ 7x - 3 = 4 \]

  5. Next, add \( 3 \) to both sides: \[ 7x - 3 + 3 = 4 + 3 \] This simplifies to: \[ 7x = 7 \]

  6. Now, divide both sides by \( 7 \): \[ x = 1 \]

The solution to the equation is \( x = 1 \).

To write the answer in set notation, we can express it as: \[ {1} \]

Therefore, the final answer is: \[ {1} \]