Select all of the equations below that are equivalent to: 3 + h = 7 Use properties of equality. Multi-select Choices: (A)3 + h + 10 = 15 (B)3 + h + 3 = 10 (C)14 + h = 12 + 7 (D)8 + h = 4 + 7

Question

Select all of the equations below that are equivalent to:  3 + h = 7 Use properties of equality.    Multi-select Choices: (A)3  +  h  +  10 = 15 (B)3  +  h  +  3 = 10 (C)14  +  h = 12  +  7 (D)8  +  h = 4  +  7

Bytelearn · Accepted Answer

Manipulate Original Equation: To determine if an equation is equivalent to 3 + h = 7, we can use properties of equality to manipulate the original equation and see if it matches any of the choices. We can add or subtract the same value from both sides of the equation without changing its equality.Check Choice (A): Let's start with choice (A): 3 + h + 10 = 15. To check if this is equivalent, we can add 10 to both sides of the original equation: (3 + h) + 10 = 7 + 10. Simplifying this gives us 3 + h + 10 = 17, which does not match choice (A).Check Choice (B): Now let's check choice (B): 3 + h + 3 = 10. Similarly, we add 3 to both sides of the original equation: (3 + h) + 3 = 7 + 3. Simplifying this gives us 3 + h + 3 = 10, which matches choice (B).Check Choice (C): Next, we look at choice (C): 14 + h = 12 + 7. We can simplify the right side of this equation: 12 + 7 = 19. So the equation becomes 14 + h = 19. To check if this is equivalent to the original equation, we can subtract 14 from both sides of the original equation: (3 + h) - 14 = 7 - 14. This simplifies to -11 + h = -7, which is not equivalent to choice (C).Check Choice (D): Finally, we examine choice (D): 8 + h = 4 + 7. Simplify the right side: 4 + 7 = 11. So the equation becomes 8 + h = 11. To check if this is equivalent to the original equation, we can add 5 to both sides of the original equation: (3 + h) + 5 = 7 + 5. This simplifies to 8 + h = 12, which is not equivalent to choice (D).

Select all of the equations below that are equivalent to: $\newline$ $3 + h = 7$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $3 + h + 10 = 15$ $\newline$ (B) $3 + h + 3 = 10$ $\newline$ (C) $14 + h = 12 + 7$ $\newline$ (D) $8 + h = 4 + 7$

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