Question

cedric and insha solved the same equation using the calculations below.
cedrics work
z - 4.5 = -1.5
z - 4.5 + 4.5 = -1.5 + 4.5
z = 3
inshas work
z - 4.5 = -1.5
z - 4.5 + (-4.5) = -1.5 + (-4.5)
z = -6
which statement is true about their work?
\bigcirc cedric is correct because he used the inverse of subtraction and added 4.5.
\bigcirc cedric is incorrect because he should have subtracted 4.5 from both sides instead of adding.
\bigcirc insha is correct because she added the opposite of 4.5, which is -4.5, to both sides.
\bigcirc insha is incorrect because she did not add -1.5 + (-4.5) correctly.

Explanation:

To solve the equation \( z - 4.5 = -1.5 \), we use the addition property of equality, which states that we can add the same number to both sides of an equation to isolate the variable. The inverse operation of subtraction is addition.

• For Cedric's work: He added \( 4.5 \) (the inverse of subtracting \( 4.5 \)) to both sides. So, \( z - 4.5 + 4.5 = -1.5 + 4.5 \), which simplifies to \( z = 3 \). This is correct.
• For Insha's work: She added \( -4.5 \) to both sides. The equation is \( z - 4.5 = -1.5 \), so adding \( -4.5 \) would be \( z - 4.5 + (-4.5)= -1.5 + (-4.5) \), which is incorrect. Also, \( -1.5 + (-4.5)= -6 \), but the main error is the operation choice.

Now let's analyze the options:

1. "Cedric is correct because he used the inverse of subtraction and added 4.5." This matches the correct method (using the inverse operation of subtraction, which is addition, to isolate \( z \)).
2. "Cedric is incorrect because he should have subtracted 4.5 from both sides instead of adding." This is wrong because subtracting \( 4.5 \) would not isolate \( z \); we need to add \( 4.5 \) to undo the subtraction of \( 4.5 \) from \( z \).
3. "Insha is correct because she added the opposite of 4.5, which is -4.5, to both sides." Adding \( -4.5 \) is incorrect here; we need to add \( 4.5 \) (the opposite of \( -4.5 \)) to both sides.
4. "Insha is incorrect because she did not add \( -1.5 + (-4.5) \) correctly." While her calculation of \( -1.5 + (-4.5) \) is \( -6 \), the bigger error is the wrong operation (adding \( -4.5 \) instead of \( 4.5 \)), but the option's reasoning is about the addition result. However, the first option is clearly correct as Cedric used the right inverse operation.

Answer:

A. Cedric is correct because he used the inverse of subtraction and added 4.5.