Question

match the justification to each statement in the solution of $x + 12.7 = -25.2$.
$x + 12.7 - 12.7 = -25.2 - 12.7$
$x = -37.9$
$x + 12.7 = -25.2$
$x + 0 = -37.9$
options:
subtraction property of equality
additive inverse/simplification
identity property of addition
given

Explanation:

1. For the equation \(x + 12.7- 12.7=-25.2 - 12.7\), we are subtracting \(12.7\) from both sides of the equation \(x + 12.7=-25.2\). This is justified by the subtraction property of equality, which states that if we subtract the same number from both sides of an equation, the equation remains true.
2. For the equation \(x=-37.9\), we simplify \(x + 12.7-12.7\) to \(x\) (since \(12.7-12.7 = 0\), using the additive inverse property where a number and its inverse add up to \(0\)) and \(-25.2-12.7=-37.9\). So this is justified by additive inverse/simplification.
3. The equation \(x + 12.7=-25.2\) is the original equation given to us, so its justification is "given".
4. For the equation \(x + 0=-37.9\), we know that \(x+12.7 - 12.7=x+(12.7-12.7)=x + 0\) (by the identity property of addition, where adding \(0\) to a number does not change the number). And \(-25.2-12.7=-37.9\), so this is justified by the identity property of addition.

Answer:

• \(x + 12.7-12.7=-25.2 - 12.7\) : subtraction property of equality
• \(x=-37.9\) : additive inverse/simplification
• \(x + 12.7=-25.2\) : given
• \(x + 0=-37.9\) : identity property of addition