Which of the following expressions is equivalent to \( 12 x=3+2 x+19 ? \) Select all that apply \( \square \) A. \( 10 x+16 \) \( \square \) B. \( 14 x+10 \) \( \square \) C. \( 2(7 x+5) \) \( \square \) D. \( 14 x+16 \) \( \square \) E. \( 17 x+13 \)

To determine which expressions are equivalent to \( 12x = 3 + 2x + 19 \), we first need to simplify the given equation. 1. **Combine like terms on the right side:** \[ 3 + 19 = 22 \] So, the equation becomes: \[ 12x = 2x + 22 \] 2. **Isolate \( x \) by moving \( 2x \) to the left side:** \[ 12x - 2x = 22 \] This simplifies to: \[ 10x = 22 \] 3. **Now, we can express this equation in different forms to compare with the options given.** - Dividing both sides by 2: \[ 5x = 11 \] - Rearranging gives: \[ 10x - 22 = 0 \] Next, we will check each option to see if they can be simplified to match \( 10x = 22 \). ### Checking the options: **A. \( 10x + 16 \)** This expression does not equal \( 0 \) when set to \( 10x - 22 \). **B. \( 14x + 10 \)** This expression does not equal \( 0 \) when set to \( 10x - 22 \). **C. \( 2(7x + 5) \)** Expanding this gives: \[ 2(7x + 5) = 14x + 10 \] This does not equal \( 10x - 22 \). **D. \( 14x + 16 \)** This expression does not equal \( 0 \) when set to \( 10x - 22 \). **E. \( 17x + 13 \)** This expression does not equal \( 0 \) when set to \( 10x - 22 \). ### Conclusion: None of the options provided are equivalent to the expression \( 12x = 3 + 2x + 19 \). Therefore, the answer is that none of the options (A, B, C, D, E) are correct.