Solve $5(x - 2) = 3x + 6$.

How we read your problem

A linear equation in x: isolate x using inverse operations.

Step-by-step solution

1. 1

   Start with the equation

   $$5~\left( x-2\right) = 3~ x+6$$
2. 2

   Simplify each side (distribute and combine like terms)

   $$5x - 10 = 3x + 6$$
3. 3

   Subtract 3x from both sides

   $$2x - 10 = 6$$
4. 4

   Add 10 to both sides

   $$2x = 16$$
5. 5

   Divide both sides by 2

   $$x = \frac{16}{2} = 8$$

Formulas used

• Linear equation

  $$ax + b = c \;\Rightarrow\; x = \frac{c - b}{a}$$

Doing the same operation to both sides keeps the equation balanced. Undoing addition, then multiplication, leaves x alone.

Verification

• x = 8: left side = 30, right side = 30 ✓