Sure, let's solve the equation step-by-step:
The given equation is:
[tex]\[ 6x + 7 = 3x + 19 \][/tex]
1. Isolate the variable terms on one side:
To start, we want to get all the [tex]\( x \)[/tex]-terms on one side of the equation. We can do this by subtracting [tex]\( 3x \)[/tex] from both sides:
[tex]\[ 6x + 7 - 3x = 3x + 19 - 3x \][/tex]
Simplify this:
[tex]\[ 3x + 7 = 19 \][/tex]
2. Isolate the constant term on the other side:
Next, we want to isolate the term with [tex]\( x \)[/tex] by getting rid of the constant on the left side. We do this by subtracting 7 from both sides of the equation:
[tex]\[ 3x + 7 - 7 = 19 - 7 \][/tex]
Simplify this:
[tex]\[ 3x = 12 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Finally, to solve for [tex]\( x \)[/tex], we need to divide both sides of the equation by 3:
[tex]\[ x = \frac{12}{3} \][/tex]
Simplify this:
[tex]\[ x = 4 \][/tex]
So, the solution to the equation [tex]\( 6x + 7 = 3x + 19 \)[/tex] is:
[tex]\[ x = 4 \][/tex]
