Solving the Equation 5x 4 = 3x 16

To solve the equation 5x + 4 = 3x + 16, we need to isolate the variable x by performing various mathematical operations. Let's go step by step to find the value of x.

Step 1: Combine Like Terms
5x + 4 = 3x + 16

In this step, we need to combine the like terms on both sides of the equation. Like terms have the same variable and exponent. Here, the like terms are 5x and 3x on the left side, and 4 and 16 on the right side.

5x - 3x + 4 = 16

Simplifying the equation, we get:
2x + 4 = 16

Step 2: Isolate the Variable
Now, we need to isolate the variable x by getting rid of the constant term on the left side of the equation. We can do this by subtracting 4 from both sides of the equation.

2x + 4 - 4 = 16 - 4

Simplifying the equation, we get:
2x = 12

Step 3: Solve for x
To solve for x, we divide both sides of the equation by the coefficient of x, which is 2.

2x/2 = 12/2

Simplifying the equation, we get:
x = 6

Step 4: Check the Solution
To ensure that the solution is correct, we substitute the value of x back into the original equation and verify if both sides are equal.

5x + 4 = 3x + 16

Substituting x = 6 into the equation, we get:
5(6) + 4 = 3(6) + 16
30 + 4 = 18 + 16
34 = 34

As both sides of the equation are equal, we can conclude that x = 6 is the correct solution to the given equation.

Final Answer:
The solution to the equation 5x + 4 = 3x + 16 is x = 6.

5x +4=3x+16
5x -3x = 16-4
2x=12
x=6