Question

solve for x.
\\(\frac{3}{8} + \frac{2x + 5}{6} = \frac{3x - 1}{24}\\)

Explanation:

Step1: Find common denominator (24)

Multiply each term by 24 to eliminate fractions:
$$24\times\frac{3}{8} + 24\times\frac{2x + 5}{6} = 24\times\frac{3x - 1}{24}$$

Step2: Simplify each term

Simplify each product:
$$3\times3 + 4\times(2x + 5) = 3x - 1$$
$$9 + 8x + 20 = 3x - 1$$

Step3: Combine like terms

Combine constants on left:
$$8x + 29 = 3x - 1$$

Step4: Isolate x terms

Subtract \(3x\) and 29 from both sides:
$$8x - 3x = -1 - 29$$
$$5x = -30$$

Step5: Solve for x

Divide by 5:
$$x = \frac{-30}{5} = -6$$

Answer:

\( x = -6 \)