Final answer:
To solve \(\frac{2}{3}(3x + 14) = 7x + 6\), multiply both sides by 3, distribute the multiplication over addition, and then isolate x to find that x equals \(\frac{2}{3}\).
Step-by-step explanation:
To solve the equation \(\frac{2}{3}(3x + 14) = 7x + 6\), we start by multiplying both sides by 3 to eliminate the fraction. Here are the steps:
Multiply both sides by 3: 3 * \(\frac{2}{3}(3x + 14)\) = 3 * (7x + 6)
Apply the distributive property: 2 * (3x + 14) = 21x + 18
Distribute the 2: 6x + 28 = 21x + 18
Subtract 6x from both sides: 28 = 15x + 18
Subtract 18 from both sides: 10 = 15x
Divide both sides by 15: x = \(\frac{10}{15}\) or x = \(\frac{2}{3}\)
Therefore, the solution to the equation is x = \(\frac{2}{3}\).
Remember, when you multiply or divide by the same number on both sides of an equation, the equality remains true, but you must apply these operations to every term.