Question

(\frac{x - 7}{2}+\frac{2x - 1}{18}=-6)

Explanation:

Step1: Eliminate the denominator

Multiply each term by 18 (the least common multiple of 2 and 18) to get rid of the fractions:
$$18\times\frac{x - 7}{2}+18\times\frac{2x - 1}{18}=18\times(-6)$$
Simplify each term:
$$9(x - 7)+(2x - 1)=- 108$$

Step2: Expand the brackets

Use the distributive property \(a(b + c)=ab+ac\) to expand \(9(x - 7)\):
$$9x-63 + 2x-1=-108$$

Step3: Combine like terms

Combine the \(x\) terms and the constant terms:
$$(9x + 2x)+(-63-1)=-108$$
$$11x-64=-108$$

Step4: Solve for \(x\)

Add 64 to both sides of the equation:
$$11x-64 + 64=-108 + 64$$
$$11x=-44$$
Divide both sides by 11:
$$x=\frac{-44}{11}$$
$$x = - 4$$

Answer:

\(x=-4\)