Question
3 Expand the brackets and simplify. \[ \frac{1}{2}(6 x-2)-3(x-1) \]
Ask by Reid Wheeler. in Saudi Arabia
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[2\]
Solution
To expand and simplify the expression:
\[
\frac{1}{2}(6x - 2) - 3(x - 1)
\]
**Step 1: Distribute the coefficients inside the brackets.**
\[
\frac{1}{2} \times 6x - \frac{1}{2} \times 2 - 3 \times x + 3 \times 1
\]
**Step 2: Perform the multiplication.**
\[
3x - 1 - 3x + 3
\]
**Step 3: Combine like terms.**
\[
(3x - 3x) + (-1 + 3) = 0x + 2 = 2
\]
**Final Answer:**
\[2\]
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Simplify this solution Bonus Knowledge
To tackle this expression, let’s first expand the brackets. Starting with \(\frac{1}{2}(6x - 2)\), we distribute the \(\frac{1}{2}\) to both terms: \[ \frac{1}{2} \cdot 6x - \frac{1}{2} \cdot 2 = 3x - 1 \] Next, we move to \(-3(x - 1)\), distributing \(-3\): \[ -3 \cdot x + 3 \cdot 1 = -3x + 3 \] Now combine your results: \[ 3x - 1 - 3x + 3 \] Simplifying this gives: \[ (3x - 3x) + (-1 + 3) = 0 + 2 = 2 \] So, the simplified expression is: \[ 2 \]
