Question

If \(a\) is multiplied by 3 and the result is 4 less than 6 times \(b,\) what is the value of \(a-2 b ?\) a. -12 b. \(-\frac{4}{3}\) c. \(-\frac{3}{4}\) d. \(\frac{4}{3}\) e. 12

Short answer

\(-\frac{4}{3}\)

Step-by-step solution

Setting Up the Equation

The equation can be written as \(3a = 6b - 4\). We can simplify this equation to find 'a' in terms of 'b'.

Solving for a

Once the equation is set up, we can find the value of 'a' as follows, \(a = \frac{6b - 4}{3}\). We reduced the equation by dividing both sides by the coefficient of 'a', which is 3.

Finding the Value of Expression

Now, we substitute the 'a' we found in terms of 'b' into the expression \(a - 2b\), which goes as follows: \(\frac{6b - 4}{3} - 2b\).

Simplifying the Expression

On simplifying the above expression, we get \(-\frac{4}{3}\). Therefore, the value of the expression \(a - 2b\) is \(-\frac{4}{3}\).