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

🏆Practice solution of an equation by multiplying/dividing both sides

With this method, we can multiply or divide both sides of the equation by the same element without thereby altering the overall value of the equation. This means that the final result of the equation will not be affected because we have multiplied or divided both sides by the same element or number.

## Test yourself on solution of an equation by multiplying/dividing both sides!

Solve the equation

$$5x-15=30$$

## Below, we provide you with some examples where we apply this method.

### Example 1

$3X=24$

We solve the equation and find the numerical value of $X$ by dividing both sides of the equation by the number $3$.

In this way, we neutralize and isolate the $X$ on the left side of the equation, while on the right side we obtain the result of the equation.

$3X=24$ / $:3$

$X=8$

The result of the equation is $8$.

### Example 2

$\frac{X}{2}=5$

We solve the equation and find the numerical value of X by multiplying both sides of the equation by the number 2. This way, we neutralize and isolate X on the left side of the equation, while on the right side we obtain the result of the equation.

$\frac{X}{2}=5$ / $\times2$

$X=10$

The result of the equation is $10$.

## Examples and exercises with solutions for solving equations by multiplying or dividing both sides by the same number

### Exercise #1

Solve the equation

$5x-15=30$

### Step-by-Step Solution

We start by moving the sections:

5X-15 = 30
5X = 30+15

5X = 45

Now we divide by 5

X = 9

$x=9$

### Exercise #2

Solve the equation

$20:4x=5$

### Step-by-Step Solution

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

$x=1$

### Exercise #3

Solve for X:

$3x=18$

### Step-by-Step Solution

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:

$x=6$

$6$

### Exercise #4

Find the value of the parameter X

$\frac{1}{3}x+\frac{5}{6}=-\frac{1}{6}$

### Step-by-Step Solution

First, we will arrange the equation so that we have variables on one side and numbers on the other side.

Therefore, we will move $\frac{5}{6}$ to the other side, and we will get

$\frac{1}{3}x=-\frac{1}{6}-\frac{5}{6}$

Note that the two fractions on the right side share the same denominator, so you can subtract them:

$\frac{1}{3}x=-\frac{6}{6}$

Observe the minus sign on the right side!

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

Now, we will try to get rid of the denominator, we will do this by multiplying the entire exercise by the denominator (that is, all terms on both sides of the equation):

$1x=-3$

$x=-3$

-3

### Exercise #5

What is the missing number?

$23-12\times(-6)+?\colon7=102$

### Step-by-Step Solution

First, we solve the multiplication exercise:

$12\times(-6)=-72$

Now we get:

$23-(-72)+x\colon7=102$

Let's pay attention to the minus signs, remember that a negative times a negative equals a positive.

We multiply them one by one to be able to open the parentheses:

$23+72+x\colon7=102$

We reduce:

$95+x:7=102$

We move the sections:

$x:7=102-95$

$x:7=7$

$\frac{x}{7}=7$

Multiply by 7:

$x=7\times7=49$

49

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