Which of the following statements are true? Select all the correct answers. If you rewrite a one-variable linear equation and see a statement like \( 4=4 \) or \( 4 a+6=4 a+6 \), then the equation has infinitely many solutions. B If you rewrite a one-variable linear equation and the variable terms are the same on each side of the equation, then you can solve the equation and find the value of the variable. C If a one-variable linear equation has one solution, then every value of the variable makes the equation true. D If both sides of a one-variable linear equation have the same variable term and different constant terms, then the equation has infinitely many solutions. E If a one-variable linear equation has no solution, then no value of the variable will make the equation true.

Let's analyze each statement one by one to determine their truthfulness. **Statement A:** If you rewrite a one-variable linear equation and see a statement like \( 4=4 \) or \( 4a+6=4a+6 \), then the equation has infinitely many solutions. - This statement is **true**. When both sides of the equation are identical, it means that the equation holds for all values of the variable, leading to infinitely many solutions. **Statement B:** If you rewrite a one-variable linear equation and the variable terms are the same on each side of the equation, then you can solve the equation and find the value of the variable. - This statement is **false**. If the variable terms are the same on both sides, the equation may reduce to a statement about constants. For example, if you have \( 3x + 2 = 3x + 5 \), it simplifies to \( 2 = 5 \), which is false. Thus, you cannot always find a unique solution. **Statement C:** If a one-variable linear equation has one solution, then every value of the variable makes the equation true. - This statement is **false**. If an equation has one solution, it means that only one specific value of the variable satisfies the equation, not every value. **Statement D:** If both sides of a one-variable linear equation have the same variable term and different constant terms, then the equation has infinitely many solutions. - This statement is **false**. If the variable terms are the same but the constant terms are different, the equation will lead to a contradiction. For example, \( 2x + 3 = 2x + 5 \) simplifies to \( 3 = 5 \), which is false. Therefore, there are no solutions. **Statement E:** If a one-variable linear equation has no solution, then no value of the variable will make the equation true. - This statement is **true**. If an equation has no solution, it means that there is no value of the variable that can satisfy the equation. ### Summary of Truthfulness: - **A:** True - **B:** False - **C:** False - **D:** False - **E:** True Thus, the correct answers are **A** and **E**.