Solving Equations Using All Methods - Examples, Exercises and Solutions

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 $5x = 0$ for $x$, we will use the following steps:

• Step 1: Identify that the equation is $5x = 0$.
• Step 2: To solve for $x$, divide both sides of the equation by 5.

Let's perform the calculation as outlined in Step 2:

$5x = 0$

Divide both sides by 5 to isolate $x$:

Simplifying, this gives:

$x = 0$

Therefore, the solution to the equation $5x = 0$ is $x = 0$.

The correct answer is option 4: $x = 0$.

To solve the equation $5x = 1$, we need to isolate $x$. Here are the steps:

• Step 1: Start with the equation $5x = 1$.
• Step 2: Divide both sides of the equation by the coefficient of $x$, which is 5, to isolate $x$. This gives us:
$\frac{5x}{5} = \frac{1}{5}$
• Step 3: Simplify the left side:
$\frac{5x}{5} = x$
• Step 4: Write the simplified equation:
$x = \frac{1}{5}$

Therefore, the solution to the equation $5x = 1$ is $x = \frac{1}{5}$.

The correct answer choice is:

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

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

• Step 1: Start with the original equation:
  $x + 5 = 8$.
• Step 2: Subtract 5 from both sides of the equation to isolate $x$:
  $x + 5 - 5 = 8 - 5$.
• Step 3: Simplify both sides:
  $x = 3$.

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

The correct answer choice is: :

3

To solve this problem, we will follow these steps:

• Step 1: Identify the given equation $3 + x = 4$.
• Step 2: Use subtraction to isolate the variable $x$.

Now, let's work through these steps:
Step 1: We have the equation: $3 + x = 4$.
Step 2: Subtract 3 from both sides of the equation to isolate $x$:

$3 + x - 3 = 4 - 3$

This simplifies to:

$x = 1$

Therefore, the solution to the equation is $x = 1$.

To solve the equation $5 - x = 4$, we aim to isolate $x$ on one side of the equation.

We start by considering the equation:
$5 - x = 4$

Step 1: Eliminate 5 from the left side to isolate terms involving $x$. To do this, subtract 5 from both sides of the equation:

$(5 - x) - 5 = 4 - 5$

Step 2: Simplify both sides:

$-x = -1$

Step 3: To solve for $x$, multiply or divide both sides by $-1$ to change the sign of $x$:

$-1 \cdot -x = -1 \cdot -1$

This simplifies to:

$x = 1$

Therefore, the solution to the equation $5 - x = 4$ is $x = 1$.

The correct answer is $x = 1$.

To solve the equation $-8 - x = -5$, we'll isolate the variable $x$ by performing algebraic operations:

Step 1: Add 8 to both sides of the equation to eliminate the $-8$:

This simplifies to:

Step 2: To solve for $x$, we need to change the sign of $x$. Multiply both sides by $-1$:

Therefore, the solution to the equation is $\boxed{-3}$.

To solve the given linear equation $-8 - x = 5$, we will follow these steps:

• Add 8 to both sides of the equation to isolate the term involving $x$.
• Subtract $x$ from both sides to further simplify; however, applying approach 1 directly cancels this step.
• Multiply both sides by -1 to solve for $x$.

First, let's add 8 to both sides of the equation:

This simplifies to:

To find $x$, multiply both sides of the equation by -1:

Therefore, the solution to the equation is $x = -13$.

To solve the equation $-5 + x = -3$, we can follow these steps:

• Step 1: We want to isolate $x$ on one side of the equation. Currently, it is subtracted by 5, so we'll eliminate the -5 by performing the operation of addition.
• Step 2: Add 5 to both sides of the equation to cancel out the -5:
  $-5 + x + 5 = -3 + 5$
• Step 3: Simplify both sides:
  $x = -3 + 5$
• Step 4: Perform the arithmetic operation on the right side:
  $x = 2$

Therefore, the solution to the problem is $x = 2$.

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 the equation $x + 3 = 5$, we will follow these steps:

• Subtract 3 from both sides of the equation to isolate $x$.
• On the left, $x + 3 - 3 = x$ remains.
• On the right, $5 - 3 = 2$.
• This gives us the equation: $x = 2$.

Therefore, the solution to the equation is $x = 2$.