Solving Equations by using Addition/ Subtraction: Monomial

To solve the equation $x + 7 = 14$, we aim to find the value of $x$ by isolating it on one side.

• Step 1: Identify the current equation: $x + 7 = 14$.
• Step 2: To isolate $x$, perform the inverse operation. Subtract 7 from both sides to maintain equality.
• Step 3: Simplify both sides: $x + 7 - 7 = 14 - 7$.
• Step 4: This simplifies to $x = 7$.

Therefore, we have found that the solution to the equation $x + 7 = 14$ is $x = 7$, which matches the given answer choice 2.

To solve the equation $x - 5 = -10$, we need to isolate $x$.

Step 1: Add 5 to both sides of the equation to cancel out the -5 on the left side.
$x - 5 + 5 = -10 + 5$
Step 2: Simplify both sides.
$x = -5$
Thus, the solution is $x = -5$.

To solve the equation $x + 9 = 3$, we need to isolate $x$.

Step 1: Subtract 9 from both sides of the equation to cancel out the +9 on the left side.
$x + 9 - 9 = 3 - 9$
Step 2: Simplify both sides.
$x = -6$
Thus, the solution is $x = -6$.

To solve the equation $x - 7 = 14$, we need to isolate $x$.

Step 1: Add 7 to both sides of the equation to cancel out the -7 on the left side.
$x - 7 + 7 = 14 + 7$
Step 2: Simplify both sides.
$x = 21$
Thus, the solution is $x = 21$.

To solve for $y$, we need to isolate it on one side of the equation. Starting with:

$y-4=9$

Add $4$ to both sides to get:

$y-4+4=9+4$

This simplifies to:

$y=13$

Therefore, the solution is $y = 13$.

To solve for $a$, we need to isolate it on one side of the equation. Starting with:

$a-5=10$

Add $5$ to both sides to get:

$a-5+5=10+5$

This simplifies to:

$a=15$

Therefore, the solution is$a = 15$.

To solve for $b$, we need to isolate it on one side of the equation. Starting with:

$b+6=14$

Subtract$6$ from both sides to get:

$b+6-6=14-6$

This simplifies to:

$b=8$

Therefore, the solution is $b = 8$.

To solve for $x$, we need to isolate it on one side of the equation. Starting with:

$x+7=12$

Subtract$7$ from both sides to get:

$x+7-7=12-7$

This simplifies to:

$x=5$

Therefore, the solution is $x = 5$.

To solve for $z$, we need to isolate it on one side of the equation. Starting with:

$z+2=8$

Subtract $2$ from both sides to get:

$z+2-2=8-2$

This simplifies to:

$z=6$

Therefore, the solution is $z = 6$.

To find the value of $a$, we must solve the given linear equation:

$11 = a - 16$

We aim to isolate $a$ by performing operations that maintain the balance of the equation. Currently, $a$ is being decreased by 16. To reverse this, we need to add 16 to both sides.

Step-by-step:

• Start with the given equation: $11 = a - 16$.
• Add 16 to both sides to start isolating $a$:

$11 + 16 = a - 16 + 16$

• This simplifies to:

$27 = a$

Thus, the value of $a$ is 27.

Therefore, the solution to the equation $11 = a - 16$ is $a = 27$.

To solve this linear equation, we need to isolate the variable $y$. Here’s how:

We start with the equation:

$6 + y = 0$

To isolate $y$, we subtract 6 from both sides of the equation. This is because we want $y$ by itself on one side of the equation:

$6 + y - 6 = 0 - 6$

On the left side, the $+6$ and $-6$ cancel each other out, leaving us with:

$y = -6$

Therefore, the solution to the equation $6 + y = 0$ is $y = -6$.

Checking our solution against the provided choices, we see that the correct answer is choice 1: $y = -6$.

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

• Step 1: Convert the mixed number $2\frac{1}{2}$ to an improper fraction.
• Step 2: Subtract $2\frac{1}{2}$ from both sides of the equation to isolate $a$.
• Step 3: Simplify the result to find the value of $a$.

Now, let's work through each step:

Step 1: Convert $2\frac{1}{2}$ to an improper fraction. $2\frac{1}{2} = \frac{5}{2}$.

Step 2: The equation becomes $a + \frac{5}{2} = 4$. To isolate $a$, subtract $\frac{5}{2}$ from both sides:

$a = 4 - \frac{5}{2}$

Step 3: Convert 4 into a fraction with the same denominator to perform the subtraction. $4 = \frac{8}{2}$.

$a = \frac{8}{2} - \frac{5}{2} = \frac{3}{2}$.

The improper fraction $\frac{3}{2}$ can be converted back to a mixed number, giving $a = 1\frac{1}{2}$.

Therefore, the solution to the problem is $a = 1\frac{1}{2}$.

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 $x + 3 = 5$, 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 $x = 2$.

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 $x + 5 = 8$, 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 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 $3 - x = 1$, we will isolate the variable $x$.

• Step 1: Subtract 3 from both sides of the equation.
  $3 - x - 3 = 1 - 3$

• Step 2: Simplify the expression.
  $-x = -2$

• Step 3: Multiply both sides by $-1$ to solve for $x$.
  $x = 2$

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

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 $x = 1$.

Let's solve the equation $17.6 - x = -11.3$ step by step:

• Step 1: Identify the need to isolate $x$ on one side. We currently have $17.6 - x = -11.3$.
• Step 2: To isolate $x$, add $x$ to both sides of the equation, resulting in $17.6 = x - 11.3$.
• Step 3: Now, add $11.3$ to both sides to solve for $x$:
  $17.6 + 11.3 = x - 11.3 + 11.3$. This simplifies further to $28.9 = x$.

Therefore, the solution to the equation is $x = 28.9$.