Solve the equation. $$ 5 x-1+2(x+1)=4 x-2 $$

Question

UpStudy AI · Accepted Answer

Certainly! Let's solve the equation step by step.

**Given Equation:**
$$ 5x - 1 + 2(x + 1) = 4x - 2 $$

**Step 1: Expand the parentheses**
$$ 2(x + 1) = 2 \cdot x + 2 \cdot 1 = 2x + 2 $$

**Step 2: Substitute the expanded form back into the equation**
$$ 5x - 1 + 2x + 2 = 4x - 2 $$

**Step 3: Combine like terms on the left side**
$$ (5x + 2x) + (-1 + 2) = 7x + 1 $$
$$ 7x + 1 = 4x - 2 $$

**Step 4: Move all terms containing $$ x $$ to one side and constant terms to the other side**
$$ 7x - 4x = -2 - 1 $$
$$ 3x = -3 $$

**Step 5: Solve for $$ x $$**
$$ x = \frac{-3}{3} $$
$$ x = -1 $$

**Solution:**
$$ x = -1 $$
$$ x = -1 $$

Solve the equation. \( 5 x-1+2(x+1)=4 x-2 \)