Algebra

Negative Signs Outside Brackets

When a negative sign appears outside a bracket, it means that every term inside the bracket is multiplied by -1. This is often referred to as distributing the negative sign. Here’s how it works:

  1. General Rule:−(a+b)=−a−b−(a+b)=−a−bThe negative sign outside the bracket changes the sign of every term inside.
  2. Examples:
    • −(x+3)=−x−3−(x+3)=−x−3
    • −(2x−5)=−2x+5−(2x−5)=−2x+5
    • −(−x+4)=x−4−(−x+4)=x−4
  3. Key Points:
    • The negative sign affects all terms inside the bracket.
    • If a term inside the bracket is positive, it becomes negative, and vice versa.
    • Always simplify the expression after distributing the negative sign.

Negative Signs Outside Brackets

When a negative sign appears outside a bracket, it means that every term inside the bracket is multiplied by -1. This is often referred to as distributing the negative sign. Here’s how it works:

  • General Rule: \( -(a + b) = -a – b \)
  • Examples:
    • \( -(x + 3) = -x – 3 \)
    • \( -(2x – 5) = -2x + 5 \)
    • \( -(-x + 4) = x – 4 \)
  • Key Points:
    • The negative sign affects all terms inside the bracket.
    • If a term inside the bracket is positive, it becomes negative, and vice versa.
    • Always simplify the expression after distributing the negative sign.

Exercises

Simplify the following expressions by distributing the negative sign. Check your answers by clicking the “Check Answer” button.

1. Simplify: \( -(x + 5) \)

2. Simplify: \( -(3x – 2) \)

3. Simplify: \( -(-4x + 7) \)

4. Simplify: \( -(2x + 6) \)

5. Simplify: \( -(-x – 3) \)

6. Simplify: \( -(5x – 8) \)

7. Simplify: \( -(-2x + 9) \)

8. Simplify: \( -(x – 10) \)

9. Simplify: \( -(-3x – 4) \)

10. Simplify: \( -(6x + 1) \)

Math Problems Leading to Equations >>

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