Question

solve \\(\frac{x + 12}{6} = -\frac{24}{9}\\).

a) -28

b) -2

c) 2

d) 28

Explanation:

Step1: Cross - multiply to eliminate fractions

To solve the equation \(\frac{x + 12}{6}=-\frac{24}{9}\), we cross - multiply. Cross - multiplying gives us \(9(x + 12)=6\times(- 24)\).

Step2: Simplify both sides

First, simplify the right - hand side: \(6\times(-24)=-144\).
Then, expand the left - hand side using the distributive property \(a(b + c)=ab+ac\), where \(a = 9\), \(b=x\) and \(c = 12\). So, \(9(x + 12)=9x+108\).
Now our equation is \(9x + 108=-144\).

Step3: Isolate the variable term

Subtract 108 from both sides of the equation: \(9x+108 - 108=-144 - 108\).
Simplifying both sides, we get \(9x=-252\).

Step4: Solve for x

Divide both sides of the equation by 9: \(\frac{9x}{9}=\frac{-252}{9}\).
Simplifying, we find that \(x=-28\).

Answer:

A) - 28