Solve (2x-1)/3 = (x+2)/4: animated lesson

1. 1. The problem
   Solving an equation

   $\frac{2~ x-1}{3} = \frac{ x+2}{4}$
2. 2. Steps, part 1
   1. $$\frac{2~ x-1}{3} = \frac{ x+2}{4}$$
      Start with the equation
   2. $$\frac{2}{3}x - \frac{1}{3} = \frac{1}{4}x + \frac{1}{2}$$
      Simplify each side (distribute and combine like terms)
   3. $$\frac{5}{12}x - \frac{1}{3} = \frac{1}{2}$$
      Subtract 1/4x from both sides
   4. $$\frac{5}{12}x = \frac{5}{6}$$
      Add 1/3 to both sides
3. 3. Steps, part 2
   1. $$x = \frac{5}{6} \div \frac{5}{12} = 2$$
      Divide both sides by 5/12 (multiply by its reciprocal)
4. 4. On the graph

5. 5. The answer
   $$x = 2$$

   x = 2

6. 6. Check
   • ✓x = 2: left side = 1, right side = 1 ✓

Solve equations with variables in the denominator and reject values that make a denominator zero.

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