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Match the justification to each statement in the solution of [tex]x + 12.7 = -25.2[/tex].

1. [tex]x + 12.7 = -25.2[/tex]
[tex]$\square$[/tex] Given

2. [tex]x + 12.7 - 12.7 = -25.2 - 12.7[/tex]
[tex]$\square$[/tex] Subtraction property of equality

3. [tex]x + 0 = -37.9[/tex]
[tex]$\square$[/tex] Additive inverse / simplification

4. [tex]x = -37.9[/tex]
[tex]$\square$[/tex] Identity property of addition


Sagot :

Alright, let's solve the equation step-by-step.

We start with the given equation:
[tex]\[ x + 12.7 = -25.2 \][/tex]

Next, we'll use the subtraction property of equality to isolate [tex]\( x \)[/tex]. The subtraction property of equality allows us to subtract the same amount from both sides of the equation:
[tex]\[ x + 12.7 - 12.7 = -25.2 - 12.7 \][/tex]

Now, we simplify both sides of the equation. On the left side, [tex]\( 12.7 - 12.7 \)[/tex] equals [tex]\( 0 \)[/tex], and on the right side, [tex]\(-25.2 - 12.7\)[/tex] equals [tex]\(-37.9\)[/tex]. This is achieved through the additive inverse property (where adding a number to its negative gives zero):
[tex]\[ x + 0 = -37.9 \][/tex]

Finally, using the identity property of addition, which states that adding zero to a number doesn’t change the value of the number, we have:
[tex]\[ x = -37.9 \][/tex]

Now, let's match the justifications to each statement in the solution:

1. Given:
[tex]\[ x + 12.7 = -25.2 \][/tex]

2. Subtraction property of equality:
[tex]\[ x + 12.7 - 12.7 = -25.2 - 12.7 \][/tex]

3. Additive inverse/simplification:
[tex]\[ x + 0 = -37.9 \][/tex]

4. Identity property of addition:
[tex]\[ x = -37.9 \][/tex]

Therefore, the matched justifications are:

[tex]\[ \begin{aligned} x + 12.7 &= -25.2 \quad & \text{(given)} \\ x + 12.7 - 12.7 &= -25.2 - 12.7 \quad & \text{(subtraction property of equality)} \\ x + 0 &= -37.9 \quad & \text{(additive inverse/simplification)} \\ x &= -37.9 \quad & \text{(identity property of addition)} \end{aligned} \][/tex]