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

To solve the equation $5x = 25$, we will isolate $x$ using division:

• Divide both sides of the equation by 5:

After performing the division, we get:

Thus, the solution to the equation is $x = 5$.

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.

To solve for $x$ in the equation $6x = 72$, follow these steps:

Step 1: Identify the equation and the coefficient of $x$.
The given equation is $6x = 72$, where the coefficient of $x$ is 6.

Step 2: Isolate $x$ by dividing both sides of the equation by the coefficient (6).
Perform the division: $x = \frac{72}{6}$.

Step 3: Simplify the result.
Calculating $\frac{72}{6}$, we get $x = 12$.

Therefore, the solution to the equation is $x = 12$.

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 $4x = \frac{1}{8}$, we need to isolate $x$. We do this by dividing both sides of the equation by the coefficient of $x$, which is 4:

• Step 1: Write the original equation: $4x = \frac{1}{8}$.
• Step 2: Divide both sides by 4 to solve for $x$:

$x = \frac{\frac{1}{8}}{4}$

• Step 3: Simplify the right-hand side by multiplying fractions, recalling that dividing by a number is equivalent to multiplying by its reciprocal:

$x = \frac{1}{8} \times \frac{1}{4} = \frac{1 \times 1}{8 \times 4} = \frac{1}{32}$

Thus, the solution to the equation is $x = \frac{1}{32}$.