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A student began solving by writing in the first line. What went wrong?

Class 8Linear Equations in One VariableLinear Equations
  • AThe 5 was multiplied only by , not by the −2 inside the bracket
  • BThe should have been transposed before opening the bracket
  • CBoth sides should have been divided by 5 before anything else
  • DThe +4 should have become −4 when the bracket was opened

Step-by-Step Solution

The distributive property multiplies the outside number by EVERY term inside: , not . The correct first line is , which leads to and . Nothing on the right-hand side changes when a bracket on the left is opened.
Answer: A) The 5 was multiplied only by , not by the −2 inside the bracket

Key idea: Equations with brackets

Open the brackets first using distributive property; then continue with the standard recipe.

Example: .

- Distribute: .
- Move left and −6 right: .
- Combine: .
- Divide by −1: .

Verify: ; . ✓

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