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

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 $y = 3\frac{6}{7}$.

The goal is to solve the equation $4 = 3y$ to find the value of $y$. To do this, we can follow these steps:

• Step 1: Divide both sides of the equation by 3 to isolate $y$.
• Step 2: Simplify the result to solve for $y$.

Now, let's work through the solution:

Step 1: We start with the equation:

$4 = 3y$

To solve for $y$, divide both sides by 3:

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

Step 2: Simplify the fraction:

$y = \frac{4}{3} = 1 \frac{1}{3}$

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

This corresponds to choice $y = 1\frac{1}{3}$ in the provided multiple-choice answers.

We begin by multiplying the simple fraction by y:

$\frac{-1}{5}\times y=-25$

We then reduce both terms by $-\frac{1}{5}$

$y=\frac{-25}{-\frac{1}{5}}$

Finally we multiply the fraction by negative 5:

$y=-25\times(-5)=125$

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 $\boldsymbol{x = -2.1}$.

To solve the given equation $4x:30 = 2$, we will follow these steps:

• Step 1: Recognize that $4x:30$ implies $\dfrac{4x}{30} = 2$.

• Step 2: Eliminate the fraction by multiplying both sides of the equation by 30.

• Step 3: Simplify the equation to solve for $x$.

Now, let's work through each step:

Step 1: The equation is written as $\dfrac{4x}{30} = 2$.

Step 2: Multiply both sides of the equation by 30 to eliminate the fraction:
$30 \times \dfrac{4x}{30} = 2 \times 30$

This simplifies to:
$4x = 60$

Step 3: Solve for $x$ by dividing both sides by 4:
$x = \dfrac{60}{4} = 15$

Therefore, the solution to the problem is $x = 15$.

Checking choices, the correct answer is:

$x = 15$

To solve the exercise, we first rewrite the entire division as a fraction:

$\frac{20}{4x}=5$

Actually, we didn't have to do this step, but it's more convenient for the rest of the process.

To get rid of the fraction, we multiply both sides of the equation by the denominator, 4X.

20=5*4X

20=20X

Now we can reduce both sides of the equation by 20 and we will arrive at the result of:

X=1

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 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 $x = 12$.

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 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 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 $\frac{1}{3}$.

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

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

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

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:

$x=6$