Solving Equations by Multiplying or Dividing Both Sides by the Same Number

We use the formula:

$a\cdot x=b$

$x=\frac{b}{a}$

We multiply the numerator by X and write the exercise as follows:

$\frac{x}{4}=3$

We multiply by 4 to get rid of the fraction's denominator:

$4\times\frac{x}{4}=3\times4$

Then, we remove the common factor from the left side and perform the multiplication on right side to obtain:

$x=12$

To solve the equation $\frac{1}{3}x = 9$, we need to isolate the variable $x$. To accomplish this, we can multiply both sides of the equation by 3, the reciprocal of $\frac{1}{3}$.

Step-by-step solution:

• Step 1: Multiply both sides by 3.
  $\left(3 \times \frac{1}{3}\right)x = 3 \times 9$
• Step 2: Simplify the left side.
  This gives us $1x = 27$, since $\left(3 \times \frac{1}{3}\right) = 1$.
• Step 3: Conclude that $x = 27$.

Therefore, the solution to the equation is $x = 27$. This matches choice number 1 from the provided options.

$ax=\frac{c}{b}$

$x=\frac{c}{b\cdot a}$

To solve the equation $6x = -12.6$, we need to isolate $x$. We achieve this by performing the following steps:

• Step 1: Identify the coefficient of $x$, which is $6$. We aim to isolate $x$ by dividing both sides of the equation by $6$.
• Step 2: Divide both sides of the equation by $6$ to solve for $x$. This will eliminate the coefficient and reveal the value of $x$.

Let's perform these calculations:

$\frac{6x}{6} = \frac{-12.6}{6}$

Simplifying both sides gives:

$x = -2.1$

Therefore, the solution to the equation is $\boldsymbol{x = -2.1}$.

We use the formula:

$a\cdot x=b$

$x=\frac{b}{a}$

Note that the coefficient of X is 3.

Therefore, we will divide both sides by 3:

$\frac{3x}{3}=\frac{18}{3}$

Then divide accordingly:

$x=6$