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

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

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:

$x=6$

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:

$x=12$

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

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

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:

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

Start by simplifying the left-hand side of the equation:

$3x - x = 2x$

So the equation becomes:

$2x = 8$

To find the value of $x$ , divide both sides by 2:

$x = \frac{8}{2}$

Then simplify the fraction:

$x = 4$

Thus, the solution to the equation is$x = 4$.

Combine like terms on the left-hand side:

$4x + 2x = 6x$

The equation becomes:

$6x = 18$

Divide both sides by 6 to solve for $x$ :

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

Simplify the division:

$x = 3$

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

To solve the equation$5x \cdot 3 = 45$, follow these steps:

1. First, identify the operation needed to solve for$x$. In this case, we have a multiplication equation.

2. Therefore, we divide both sides of the equation by 15 (since $5 \times 3 = 15$) to isolate $x$:

$x = \frac{45}{15}$

3. Calculate $x$:

$x = 3$

To solve the equation $6x \cdot 2 = 24$, follow these steps:

1. First, identify the operation involved. In this case, it is multiplication.

2. Divide both sides of the equation by 12 (since $6 \times 2 = 12$) to isolate $x$:

$x = \frac{24}{12}$

3. Calculate $x$:

$x = 2$

To solve for $x$, we start with the equation:
$25 + 75 = 10x$

The left side simplifies to:
$100 = 10x$

To isolate $x$, divide both sides by 10:
$\frac{100}{10} = x$

$x = 10$, which simplifies to:
$x = 5$

To solve for $x$, we start with the equation:
$50 + 10 = 2x$

The left side simplifies to:
$60 = 2x$

To isolate $x$, divide both sides by 2:
$\frac{60}{2} = x$

$x = 30$

To solve for $x$, we start with the equation:
$10 + 140 = 30x$

The left side simplifies to:
$150 = 30x$

To isolate $x$, divide both sides by 30:
$\frac{150}{30} = x$

$x = 5$, which simplifies to:
$x = 4$

To solve the equation $5x \cdot 6 = 90$, start by simplifying the left side of the equation:

Divide both sides by 6 to isolate $5x$:

$5x = \frac{90}{6}$

This simplifies to:

$5x = 15$

Next, divide both sides by 5 to solve for $x$:

$x = \frac{15}{5}$

This gives us:

$x = 3$

To solve the equation $7x \cdot 4 = 56$, start by simplifying the right side of the equation:

Divide both sides by 4 to isolate $7x$:

$7x = \frac{56}{4}$

This simplifies to:

$7x = 14$

Next, divide both sides by 7 to solve for $x$:

$x = \frac{14}{7}$

This gives us:

$x = 2$

We start by moving the sections:

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

5X = 45

Now we divide by 5

X = 9