To solve the equation [tex]\( 7 - 2x - \frac{-1 - 3x}{7} = 2 - \frac{2x - 1}{3} \)[/tex], we need to find the value of [tex]\( x \)[/tex]. We'll go through the steps to isolate [tex]\( x \)[/tex] and find its value.
1. Write down the given equation:
[tex]\( 7 - 2x - \frac{-1 - 3x}{7} = 2 - \frac{2x - 1}{3} \)[/tex].
2. Combine like terms and fractions:
To eliminate the fractions, we can find a common denominator which is 21 (since 7 and 3 are the denominators).
3. Clear the fractions by multiplying every term by 21:
[tex]\[
21 \left( 7 - 2x - \frac{-1 - 3x}{7} \right) = 21 \left( 2 - \frac{2x - 1}{3} \right)
\][/tex]
Simplify:
[tex]\[
21 \cdot 7 - 21 \cdot 2x - 21 \cdot \frac{-1 - 3x}{7} = 21 \cdot 2 - 21 \cdot \frac{2x - 1}{3}
\][/tex]
[tex]\[
147 - 42x - 3(-1 - 3x) = 42 - 7(2x - 1)
\][/tex]
4. Simplify inside the parentheses:
[tex]\[
147 - 42x + 3 + 9x = 42 - 14x + 7
\][/tex]
[tex]\[
147 - 42x + 3 + 9x = 42 - 14x + 7
\][/tex]
Combine like terms:
[tex]\[
150 - 33x = 49 - 14x
\][/tex]
5. Move all terms involving [tex]\( x \)[/tex] to one side and constant terms to the other side:
[tex]\[
150 - 49 = 33x - 14x
\][/tex]
6. Combine the constants and the coefficients of [tex]\( x \)[/tex]:
[tex]\[
101 = 19x
\][/tex]
7. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{101}{19}
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\(\frac{101}{19}\)[/tex], which is approximately 5.32. Therefore, the correct answer is:
B) 5.32
