Solving Equations by using Addition/ Subtraction: Binomial

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

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
$x = 5$.

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:

$x = 5$

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 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, $x = 0$.

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:
$11 - 3 = 8$
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 $5 + x - 3 = 2 + 1$, 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, $x = 1$.

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 the equation $9x - 3 = 10x + 1$, we need to get all terms with $x$ on one side and constant terms on the other side. Here's how we do it step-by-step:

• First, subtract $9x$ from both sides of the equation to start getting $x$ terms on one side. This gives us: $-3 = x + 1$

• Next, subtract 1 from both sides to isolate $x$. We get: $-3 - 1 = x$

• Simplifying the left side, we find: $x = -4$

Therefore, the solution is $x = -4$.

We start with the equation:
$4x + 4 = 5x + 2$

Our goal is to solve for $x$. To do this, we aim to collect all terms containing $x$ on one side of the equation and constant terms on the other side. First, subtract $4x$ from both sides of the equation to eliminate the $x$ term on the left side:

$4x + 4 - 4x = 5x + 2 - 4x$

This simplifies the equation to:

$4 = x + 2$

Next, subtract $2$ from both sides to isolate the variable $x$ on the right side:

$4 - 2 = x + 2 - 2$

This gives us:

$2 = x$

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

To solve the equation $3x + 5 = 2x + 20$, we need to find the value of $x$ that satisfies this equation. Here are the detailed steps:

• Step 1: Eliminate the variable from one side.
  We want to get all terms involving $x$ on one side and constant terms on the other side. First, subtract $2x$ from both sides of the equation to eliminate $x$ from the right side.

  $3x + 5 - 2x = 2x + 20 - 2x$

  This simplifies to:

  $x + 5 = 20$

• Step 2: Simplify the equation.
  Now, we need to isolate $x$ by removing the constant term from the left side. Subtract 5 from both sides:

  $x + 5 - 5 = 20 - 5$

  This simplifies to:

  $x = 15$

• Step 3: Verify the solution.
  Substitute $x = 15$ back into the original equation to check if it holds true:

  $3(15) + 5 = 2(15) + 20$

  This results in:

  $45 + 5 = 30 + 20$

  $50 = 50$

  Since both sides of the equation are equal,$x = 15$ is indeed the correct solution.

Therefore, the solution to the equation $3x + 5 = 2x + 20$ is $x = 15$.