Solve for X: 2x+45-1/3x=5(x+7) Linear Equation

To solve this problem, we'll follow these steps:

• Step 1: Distribute on the right-hand side
• Step 2: Combine like terms on the left-hand side
• Step 3: Isolate the variable $x$
• Step 4: Solve for $x$

Now, let's work through each step:

Step 1: Distribute on the right-hand side of the equation:

$2x + 45 - \frac{1}{3}x = 5(x + 7) \quad \Rightarrow \quad 2x + 45 - \frac{1}{3}x = 5x + 35$

Step 2: Combine like terms on the left-hand side:

Combine $2x$ and $-\frac{1}{3}x$ on the left:

$2x - \frac{1}{3}x = \frac{6}{3}x - \frac{1}{3}x = \frac{5}{3}x$

The equation becomes:

$\frac{5}{3}x + 45 = 5x + 35$

Step 3: Move all terms with $x$ to one side and constants to the other:

$\frac{5}{3}x - 5x = 35 - 45$

Step 4: Simplify and solve for $x$:

$\frac{5}{3}x - \frac{15}{3}x = -10$ $-\frac{10}{3}x = -10$

Step 5: Solve for $x$ by dividing both sides by $-\frac{10}{3}$:

$x = \frac{-10}{-\frac{10}{3}} = 3$

Therefore, the solution to the problem is $x = 3$.