If -12 × (-3) + [20 ÷ (-4) – (-24) ÷ 8] – [16 ÷ (-2)] = (-28 ÷ 7) + x, then…

Concept

Simplify using the standard order of operations (BODMAS): work out everything inside a bracket first, carrying out any division before addition or subtraction within it, and evaluate the two square brackets independently before combining them from left to right. When dividing two integers, like signs give a positive quotient and unlike signs give a negative quotient, and subtracting a negative number is the same as adding its positive value.

Application

1. Evaluate the product outside the brackets first: −12 × (−3) = 36, since a negative multiplied by a negative gives a positive.

2. Evaluate the two divisions inside the first square bracket: 20 ÷ (−4) = −5, and (−24) ÷ 8 = −3.

3. Combine the first bracket using these results: −5 − (−3) = −5 + 3 = −2.

4. Evaluate the second square bracket: 16 ÷ (−2) = −8.

5. Combine the left-hand side of the equation: 36 + (−2) − (−8) = 36 − 2 + 8 = 42.

6. Simplify the constant on the right-hand side: −28 ÷ 7 = −4, so the equation reduces to 42 = −4 + x.

7. Solve for x by adding 4 to both sides: x = 42 + 4 = 46.

Cross-check

Substitute x = 46 back into the right-hand side: −4 + 46 = 42, which matches the left-hand side total found above, confirming the value.