Answered

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Solve for [tex]\( x \)[/tex].

[tex]\[ 4(2x - 3) = 9 - 3(2 + x) \][/tex]

A. [tex]\( x = 3 \)[/tex]

B. [tex]\( x = \frac{15}{11} \)[/tex]

C. [tex]\( x = 0 \)[/tex]

D. [tex]\( x = \frac{15}{6} \)[/tex]

Sagot :

GinnyAnswer
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]
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