Solving an Equation by Multiplication/ Division - Examples, Exercises and Solutions

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 $x = \frac{1}{32}$.

To solve the equation $-6x = 18$, we need to isolate the variable $x$.

Our equation is:

$-6x = 18$

The variable $x$ is multiplied by $-6$. To undo this operation and solve for $x$, we divide both sides of the equation by $-6$. This will isolate $x$ on one side of the equation:

$\frac{-6x}{-6} = \frac{18}{-6}$

Simplifying both sides, we find:

$x = -3$

Thus, the solution to the equation $-6x = 18$ is $x = -3$.

Therefore, the correct answer is $x = -3$.

To solve the equation $-7y = -27$, we need to isolate the variable $y$. We do this by performing the following steps:

• Step 1: Divide both sides of the equation by $-7$ to solve for $y$.

Performing this operation gives us:

Simplifying both sides, we have:

To express $\frac{27}{7}$ as a mixed number, we divide 27 by 7:

• 27 divided by 7 equals 3 with a remainder of 6. Hence, $\frac{27}{7} = 3\frac{6}{7}$.

Therefore, the solution to the equation is $y = 3\frac{6}{7}$.

Among the given choices, option 1 matches our result.

Therefore, the solution to the problem is $y = 3\frac{6}{7}$.

To solve this problem, we will follow the steps outlined below:

• Step 1: Recognize that $\frac{1}{5}x = 12$ gives us $x$ multiplied by $\frac{1}{5}$.
• Step 2: Multiply both sides of the equation by 5 to eliminate the fraction.
• Step 3: Simplify the resulting equation to solve for $x$.

Let's proceed step-by-step:

Step 1: We have the equation $\frac{1}{5}x = 12$.

Step 2: To isolate $x$, multiply both sides of the equation by 5:

$5 \times \frac{1}{5}x = 5 \times 12$

Step 3: Simplify both sides:

• The left side simplifies to $x$ because $5 \times \frac{1}{5} = 1$, so $x$ is left alone.
• The right side becomes $60$, since $5 \times 12 = 60$.

Therefore, the value of $x$ is $60$.

Therefore, the solution to the problem is $x = 60$.

To solve the equation $7x = 4$, we will follow these steps:

• Step 1: We start with the equation $7x = 4$.

• Step 2: Our goal is to isolate $x$. Since $x$ is multiplied by 7, we will divide both sides of the equation by 7.

• Step 3: Performing division: $x = \frac{4}{7}$

Therefore, the solution to the equation $7x = 4$ is $x = \frac{4}{7}$.

To solve the equation $6x = 3$, follow these steps:

Step 1: We aim to isolate $x$. Divide both sides of the equation by 6 to remove the coefficient attached to $x$:

Step 2: Simplify the fraction on the right side:

Therefore, the solution to the equation $6x = 3$ is $x = \frac{1}{2}$.

To solve this problem, we'll follow these steps:

• Identify the given fraction equation.
• Multiply both sides of the equation by the reciprocal of the coefficient of $x$.
• Simplify to isolate $x$.

Now, let's work through these steps:
Step 1: The problem gives us the equation $\frac{1}{3} x = \frac{1}{9}$.
Step 2: We multiply both sides by 3 to eliminate the fraction on the left side:

$3 \times \frac{1}{3} x = 3 \times \frac{1}{9}$

Step 3: Simplifying both sides results in:

$x = \frac{3}{9}$

Further simplification of $\frac{3}{9}$ yields:

$x = \frac{1}{3}$

Therefore, the solution to the problem is $\frac{1}{3}$.

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:

$x=6$

To solve the equation $5x = 3$, we will isolate $x$ by using division:

• Step 1: Recognize that $x$ is multiplied by 5. To isolate $x$, we need to undo this multiplication.
• Step 2: Divide both sides of the equation by 5. This step uses the Division Property of Equality:

$\frac{5x}{5} = \frac{3}{5}$

Step 3: Simplify both sides. The left side simplifies to $x$ (because $\frac{5x}{5} = x$), and the right side is $\frac{3}{5}$.

Hence, the solution to the equation $5x = 3$ is $x = \frac{3}{5}$.

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

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

To solve the equation $8x = 5$, follow these steps:

• Step 1: Identify the equation $8x = 5$, where $x$ is the unknown variable.
• Step 2: To isolate $x$, divide both sides of the equation by 8.
  This step involves equivalent operations to maintain equality.
• Step 3: Perform the division on both sides:
  $\frac{8x}{8} = \frac{5}{8}$.
  This simplifies to $x = \frac{5}{8}$.

Now, let's outline these steps in detail:

We begin with the equation $8x = 5$.

Dividing both sides by the coefficient of $x$, which is 8, gives:

$\frac{8x}{8} = \frac{5}{8}$.

This simplifies directly to:

$x = \frac{5}{8}$.

Therefore, the solution to the problem is $x = \frac{5}{8}$.