Let's solve the given equation step-by-step without using the Python code reference and ensuring the solution is presented as if derived by manual calculations.
Given the equation:
[tex]\[ 4(2x - 3) = 9 - 3(2 + x) \][/tex]
Let's simplify and solve it step-by-step:
1. Distribute the constants inside the parentheses:
[tex]\[ 4 \cdot (2x) - 4 \cdot 3 = 9 - 3 \cdot 2 - 3 \cdot x \][/tex]
[tex]\[ 8x - 12 = 9 - 6 - 3x \][/tex]
2. Simplify the terms on both sides:
[tex]\[ 8x - 12 = 3 - 3x \][/tex]
3. Move the terms involving [tex]\( x \)[/tex] to one side and the constant terms to the other side. Add [tex]\( 3x \)[/tex] to both sides:
[tex]\[ 8x + 3x - 12 = 3 \][/tex]
[tex]\[ 11x - 12 = 3 \][/tex]
4. Add 12 to both sides to isolate the [tex]\( x \)[/tex]-terms:
[tex]\[ 11x - 12 + 12 = 3 + 12 \][/tex]
[tex]\[ 11x = 15 \][/tex]
5. Divide both sides by 11 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{15}{11} \][/tex]
So the solution to the equation [tex]\( 4(2x - 3) = 9 - 3(2 + x) \)[/tex] is:
[tex]\[ x = \frac{15}{11} \][/tex]
