Solving Equations by using Addition/ Subtraction: Binomial

Step-by-step solution:

1. Begin with the equation: $x + 9 = 15$

2. Subtract 9 from both sides: $x + 9 - 9 = 15 - 9$, which simplifies to $x = 6$

To solve for $x$, start by isolating $x$ on one side of the equation:
Subtract 7 from both sides:
$x + 7 - 7 = 12 - 7$ simplifies to
$x = 5$.

To solve for $x$, start by isolating $x$ on one side of the equation:
Subtract 8 from both sides:
$x + 8 - 8 = 10 - 8$ simplifies to
$x = 2$.

To solve for $x$, start by isolating $x$ on one side of the equation:
Subtract 3 from both sides:
$x + 3 - 3 = 7 - 3$ simplifies to
$x = 4$.

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 $6 - x = 10 - 2$, 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 $x=2$.

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 $x = 0$.

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:
$10 - 6 = 4$
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 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 $5 + x - 3 = 2 + 1$, 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 $3 + x + 1 = 6 - 2$, 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$2 + x - 5 = 4 - 3$, 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,$x = 4$.

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 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:

$x = 4$

To solve the equation $x + 3 = -5 + 2x$, we will proceed with these steps:

• Step 1: Simplify and rearrange the terms.
• Step 2: Isolate the variable $x$.
• Step 3: Solve for $x$.

Let's go through each of these steps.

Step 1: Simplify the equation by moving all terms involving $x$ to one side and constant terms to the other. Subtract $x$ from both sides:
$x + 3 - x = -5 + 2x - x$
This simplifies to:
$3 = -5 + x$

Step 2: Add 5 to both sides to isolate $x$:
$3 + 5 = x$

Step 3: Simplify the result:
$8 = x$

Therefore, the solution to the equation is $x = 8$.

To solve the equation $6 - 7x = -5x + 8$, we will follow these steps:

• Step 1: Move all terms involving $x$ to one side of the equation by adding $5x$ to both sides.
• Step 2: Simplify both sides of the equation.
• Step 3: Solve for $x$.

Now, let's work through each step:

Step 1: Add $5x$ to both sides to move the $x$-term to the left side:

$6 - 7x + 5x = 8$

Step 2: Simplify the equation by combining the $x$-terms on the left side:

$6 - 2x = 8$

Step 3: To isolate $-2x$ on the left, subtract $6$ from both sides:

$-2x = 8 - 6$

Simplify the right side:

$-2x = 2$

Finally, divide both sides by $-2$ to solve for $x$:

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

$x = -1$

Therefore, the solution to the problem is $x = -1$.

To solve for $x$, first, we need to get all terms involving $x$ on one side of the equation and constant terms on the other. Start with the original equation:

$2x + 4 = 3x - 5$

Subtract $2x$ from both sides to isolate the term involving $x$ on one side:

$4 = x - 5$

Next, add 5 to both sides to isolate $x$:

$9 = x$

Thus, the value of $x$ is $9$.