Question

Solve each of the given equations for \(x .\) Check your answers by hand or with a calculator $$3 x-14=6 x+4$$

Short answer

Answer: The solution to the given linear equation is $$x = -6$$.

Step-by-step solution

Identify the problem

We are given the following linear equation: $$3 x - 14 = 6 x +4$$ Our goal is to determine the value of x that makes this equation true.

Move terms with x to one side

To simplify the equation, we need to move all terms containing x to one side of the equation. To do this, we can subtract 3x from both sides: $$3 x - 14 - 3 x = 6 x + 4 - 3 x$$ This simplifies to: $$-14 = 3x+4$$

Move the constant term to the other side

Now, we will move the constant term (+4) to the other side by subtracting 4 from both sides of the equation: $$-14 - 4 = 3x + 4 - 4$$ This simplifies to: $$-18 = 3x$$

Solve for x

To find the value of x, we can divide both sides of the equation by 3: $$\frac{-18}{3} = \frac{3x}{3}$$ This simplifies to: $$-6 = x$$

Check the answer

Now that we have found the value of x, we can check if our answer is correct by plugging it back into the original equation: $$3 (-6) - 14 = 6 (-6) + 4$$ This simplifies to: $$-18-14=-36+4$$ Since both sides of the equation simplify to the same value, we can confirm that our solution is correct. The solution to the equation is: $$x = -6$$