Linear Equations (One Variable) - Examples, Exercises and Solutions

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 $x + 5 = 8$, 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 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 $10 + 3x = 19$, follow these steps:

• Step 1: Subtract 10 from both sides of the equation to begin isolating $x$:
• $10 + 3x - 10 = 19 - 10$
• This simplifies to $3x = 9$.
• Step 2: Divide both sides by 3 to solve for $x$:
• $\frac{3x}{3} = \frac{9}{3}$
• This reduces to $x = 3$.

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

To solve the equation $24 - 8x = -2x$, we need to isolate $x$. Follow these steps:

• Step 1: Move all terms involving $x$ to one side of the equation. Add $8x$ to both sides to get:
  $24 = 8x - 2x$
• Step 2: Simplify the equation by combining like terms on the right:
  $24 = 6x$
• Step 3: Solve for $x$ by dividing both sides by 6:
  $x = \frac{24}{6}$
• Step 4: Simplify the result:
  $x = 4$

Therefore, the solution to the problem is $\mathbf{x = 4}$.

To solve$2 + x - 5 = 4 - 3$, we first simplify both sides:

Left side:
$2 - 5 + x = -3 + x$

Right side:
$4 - 3 = 1$

Now the equation is $-3 + x = 1$.

Add 3 to both sides:
$x = 1 + 3$

So,$x = 4$.

To solve the given linear equation $33x - 11x = 66$, we will follow these steps:

• Simplify the equation by combining like terms.
• Isolate the variable $x$ to find its value.

Here's how we approach it:

Step 1: Combine like terms on the left-hand side of the equation.

We have $33x - 11x$. By combining these terms, we calculate:

$33x - 11x = (33 - 11)x = 22x$.

Our equation now simplifies to $22x = 66$.

Step 2: Isolate $x$ by dividing both sides of the equation by 22.

When we divide both sides of the equation by 22, we get:

$x = \frac{66}{22}$.

By performing the division, we find $x = 3$.

Therefore, the value of $x$ that satisfies the equation $33x - 11x = 66$ is $x = 3$.

First, simplify the right side of the equation:
$10 - 6 = 4$
Hence, the equation becomes $3 - x = 4$.
Subtract 3 from both sides to isolate $x$:
$3 - x - 3 = 4 - 3$
This simplifies to:
$-x=1$
Divide by -1 to solve for$x$:
$x=-1$
Therefore, the solution is $x = 1$.

To solve $3 + x + 1 = 6 - 2$, we first simplify both sides:

Left side:
$3 + 1 + x = 4 + x$

Right side:
$6 - 2 = 4$

Now the equation is $4 + x = 4$.

Subtract 4 from both sides:
$x = 4 - 4$

So, $x = 0$.

First, simplify both sides of the equation:

Left side: $3 + x - 2 = 1 + x$

Right side: $7 - 3 = 4$

So the equation becomes:

$1 + x = 4$

Next, isolate $x$ by subtracting 1 from both sides:

$1 + x - 1 = 4 - 1$

This simplifies to:

$x = 3$

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 $3x - 5 = 10$, we follow these steps:

• Add $5$ to both sides of the equation to eliminate the $-5$:
  $3x - 5 + 5 = 10 + 5$
  Simplifies to:
  $3x = 15$
• Next, divide both sides of the equation by $3$ to solve for $x$:
  $\frac{3x}{3} = \frac{15}{3}$
  This results in:
  $x = 5$

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

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

• Step 1: Simplify the given equation by combining like terms.
• Step 2: Isolate the variable $x$ on one side of the equation.
• Step 3: Solve the resulting simplified equation for $x$.

Now, let's work through each step:

Step 1: Simplify the given equation:

The original equation is: $3 - x + 7 = 5$.

Combine like terms on the left side of the equation:

$3 + 7 = 10$, so the equation becomes:

$10 - x = 5$.

Step 2: Isolate the variable $x$:

Subtract 10 from both sides of the equation to move the constant term:

$-x = 5 - 10$.

Simplify the right side:

$-x = -5$.

Step 3: Solve for $x$:

Multiply both sides of the equation by $-1$ to solve for $x$:

$x = 5$.

Therefore, the solution to the problem is $x = 5$.

First, simplify the right side of the equation:
$12 - 4 = 8$
Hence, the equation becomes $5 - x = 8$.
Subtract 5 from both sides to isolate $x$:
$5 - x - 5 = 8 - 5$
This simplifies to:
$-x=3$
Divide by -1 to solve for $x$:
$x=-3$
Therefore, the solution is $x=-3$.

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 $x = 5$.