Certainly! Let's solve the equation step-by-step:
Given equation:
[tex]\[ 3x + \frac{1}{2}x + 6 = 2x \][/tex]
1. Combine like terms on the left side:
- Here, we can add the [tex]\(3x\)[/tex] and [tex]\(\frac{1}{2}x\)[/tex]:
[tex]\[ 3x + \frac{1}{2}x = \frac{6x}{2} + \frac{1x}{2} = \frac{7x}{2} \][/tex]
So, the equation simplifies to:
[tex]\[ \frac{7x}{2} + 6 = 2x \][/tex]
2. Isolate the variable term(s):
- We'll first eliminate the fraction by multiplying every term by 2 to make the calculations simpler:
[tex]\[ 2 \cdot \frac{7x}{2} + 2 \cdot 6 = 2 \cdot 2x \][/tex]
[tex]\[ 7x + 12 = 4x \][/tex]
3. Move all terms involving [tex]\(x\)[/tex] to one side:
- Subtract [tex]\(4x\)[/tex] from both sides to bring all [tex]\(x\)[/tex]-terms to the left:
[tex]\[ 7x - 4x + 12 = 0 \][/tex]
[tex]\[ 3x + 12 = 0 \][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Now, isolate [tex]\(x\)[/tex] by moving the constant term to the right side:
[tex]\[ 3x + 12 - 12 = -12 \][/tex]
[tex]\[ 3x = -12 \][/tex]
- Finally, divide both sides by 3:
[tex]\[ x = \frac{-12}{3} \][/tex]
[tex]\[ x = -4 \][/tex]
Thus, the solution to the equation [tex]\(3x + \frac{1}{2}x + 6 = 2x\)[/tex] is:
[tex]\[ x = -4 \][/tex]
