Certainly! Let's solve the equation step-by-step:
Given equation:
[tex]\[ 3x - 6(5x + 3) = 9x + 6 \][/tex]
1. Distribute the 6 on the left side:
[tex]\[ 3x - 6(5x + 3) \][/tex]
This becomes:
[tex]\[ 3x - 6 \cdot 5x - 6 \cdot 3 \][/tex]
[tex]\[ 3x - 30x - 18 \][/tex]
So, we have:
[tex]\[ 3x - 30x - 18 = 9x + 6 \][/tex]
2. Combine like terms on the left side:
[tex]\[ 3x - 30x = -27x \][/tex]
So, the equation becomes:
[tex]\[ -27x - 18 = 9x + 6 \][/tex]
3. Move all terms involving x to one side and constants to the other:
To isolate the terms involving [tex]\(x\)[/tex], we need to move [tex]\(9x\)[/tex] from the right to the left side and move [tex]\(-18\)[/tex] from the left to the right side:
[tex]\[ -27x - 9x = 6 + 18 \][/tex]
Combining the terms:
[tex]\[ -36x = 24 \][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by -36:
[tex]\[ x = \frac{24}{-36} \][/tex]
Thus:
[tex]\[ x = -\frac{2}{3} \][/tex]
[tex]\[ x \approx -0.6666666666666666 \][/tex]
So, the solution to the equation [tex]\( 3x - 6(5x + 3) = 9x + 6 \)[/tex] is [tex]\( x = -\frac{2}{3} \)[/tex] or approximately [tex]\( -0.6666666666666666 \)[/tex].
