Solving Equations Using All Methods: Rearranging Equations

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:

$x = 3$

First, simplify both sides of the equation:

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

Right side: $8 - 2 = 6$

Now the equation is: $x + 2 = 6$

Subtract 2 from both sides to isolate $x$:

$x + 2 - 2 = 6 - 2$

Simplifying gives:

$x = 4$

First, simplify both sides of the equation:

Left side: $x + 4 - 2 = x + 2$

Right side: $6 + 1 = 7$

Now the equation is: $x + 2 = 7$

Subtract 2 from both sides to isolate$x$:

$x + 2 - 2 = 7 - 2$

Simplifying gives:

$x = 5$

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 $x = 1$.

First, simplify the right side of the equation:
$11 - 3 = 8$
Hence, the equation becomes $8 - x = 8$.
Subtract 8 from both sides to isolate $x$:
$8 - x - 8 = 8 - 8$
This simplifies to:
$-x=0$
Divide by -1 to solve for $x$:
$x = 0$
Therefore, the solution is $x = 0$.

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 $x=-3$.

First, simplify the right side of the equation:
$15 - 5 = 10$
Hence, the equation becomes $7 - x = 10$.
Subtract 7 from both sides to isolate $x$:
$7 - x - 7 = 10 - 7$
This simplifies to:
$-x=3$
Divide by -1 to solve for$x$:
$x=-3$
Therefore, the solution is $x=-3$.

First, simplify the right side of the equation:
$16 - 7 = 9$
Hence, the equation becomes $9 - x = 9$.
Since both sides are equal, $x$ must be $0$.
Therefore, the solution is $x = 0$.

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 $3 + x + 1 = 6 - 2$, 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, $x = 0$.

To solve $5 + x - 3 = 2 + 1$, we first simplify both sides:

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

Right side:
$2 + 1 = 3$

Now the equation is $2 + x = 3$.

Subtract 2 from both sides:
$x = 3 - 2$

So, $x = 1$.

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 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 the equation $6 - x = 10 - 2$, follow these steps:

1. First, simplify both sides of the equation:

2. On the right side, calculate $10 - 2 = 8$.

3. The equation simplifies to $6 - x = 8$.

4. To isolate x, subtract 6 from both sides:

5. $6 - x - 6 = 8 - 6$

6. This simplifies to $-x = 2$.

7. Multiply both sides by -1 to solve for x:

8. $x = -2 \times -1 = 2$.

9. Since the problem requires only manipulation by transferring terms, the initial approach to the equation setup should lead to x = 4 as the solution before re-evaluation.

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

To solve the equation $-8x + 3 = -29$, we'll follow these steps:

• Step 1: Subtract 3 from both sides of the equation to eliminate the constant on the left side.
• Step 2: Divide both sides by $-8$, the coefficient of $x$, to solve for $x$.

Let's apply these steps:
Step 1: Subtract 3 from both sides:
$-8x + 3 - 3 = -29 - 3$
This simplifies to:
$-8x = -32$

Step 2: Divide both sides by $-8$ to isolate $x$:
$\frac{-8x}{-8} = \frac{-32}{-8}$
This results in:
$x = 4$

Therefore, the solution to the equation is $x = 4$, which corresponds to choice 4.

To solve the given equation $7x + 5.5 = 19.5$, we'll follow these steps:

• Step 1: Eliminate the constant term from the left side by subtracting 5.5 from both sides of the equation.
• Step 2: Simplify the equation after subtraction to isolate the term with $x$.
• Step 3: Use division to solve for $x$.

Now, let's work through each step:

Step 1: Subtract 5.5 from both sides.

We have:
$7x + 5.5 - 5.5 = 19.5 - 5.5$

This simplifies to:
$7x = 14$

Step 2: Divide both sides by 7 to solve for $x$.

So, we divide by 7:
$\frac{7x}{7} = \frac{14}{7}$

This simplifies to:
$x = 2$

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

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 $x = 5$.

To solve the equation $\frac{1}{5}x - 4 = 6$, we will follow these steps:

• Step 1: Add 4 to both sides of the equation to eliminate the subtraction and isolate the fractional term.
• Step 2: Multiply both sides by 5 to clear the fraction and solve for $x$.

Let's apply these steps to solve the equation:

Step 1: Add 4 to both sides:
$\frac{1}{5}x - 4 + 4 = 6 + 4$
This simplifies to:
$\frac{1}{5}x = 10$

Step 2: Multiply both sides by 5 to solve for $x$:
$5 \times \frac{1}{5}x = 10 \times 5$
This simplifies to:
$x = 50$

Therefore, the solution to the equation is $x = 50$.

To solve the equation $\frac{2}{8}x - 3 = 7$, we'll follow these steps:

• Step 1: Simplify the fraction. The coefficient $\frac{2}{8}$ simplifies to $\frac{1}{4}$.
• Step 2: Eliminate the constant term by adding 3 to both sides of the equation.
• Step 3: Solve for $x$ by removing the coefficient of $x$ using division.

Let's solve the equation step-by-step:

Step 1: Simplify the equation:
The equation $\frac{2}{8}x - 3 = 7$ simplifies to $\frac{1}{4}x - 3 = 7$.

Step 2: Eliminate the constant term:
Add 3 to both sides to isolate the term involving $x$:

$\frac{1}{4}x - 3 + 3 = 7 + 3$

This simplifies to:

$\frac{1}{4}x = 10$

Step 3: Solve for $x$:
Multiply both sides by the reciprocal of $\frac{1}{4}$ to solve for $x$:

$4 \cdot \frac{1}{4}x = 4 \cdot 10$

This simplifies to:

$x = 40$

Therefore, the solution to the equation is $x = 40$.