Simplifying and Combining Like Terms - Examples, Exercises and Solutions

Let's combine all the x terms together:

$7x+4x+5x=11x+5x=16x$

The resulting equation is:

$16x=0$

Now let's divide both sides by 16:

$\frac{16x}{16}=\frac{0}{16}$

$x=\frac{0}{16}=0$

To solve this problem, we'll proceed with the following steps:

• Step 1: Combine like terms of the given equation.
• Step 2: Solve for the variable $m$.

Now, let's work through these steps:

Step 1: Combine like terms:
We start with the equation $7m + 3m - 40m = 0$.
Combining these like terms entails adding or subtracting the coefficients of $m$:

$(7 + 3 - 40)m = 0$
Calculate the sum and difference of these coefficients:
$(10 - 40)m = 0$

This simplifies to:
$-30m = 0$

Step 2: Solve for $m$:
To isolate $m$, divide both sides by $-30$:
$m = \frac{0}{-30}$

Calculate the right-hand side:

$m = 0$

Therefore, the solution to the problem is $m = 0$. This corresponds to choice 3 from the provided answer options.

To solve the equation $2a + 3a + 45a = 0$, follow these steps:

• Step 1: Combine Like Terms.

Add the coefficients of $a$:

$2 + 3 + 45 = 50$

• Step 2: Substitute and Simplify.

This simplifies the equation to:

$50a = 0$

• Step 3: Solve for $a$.

To find $a$, divide both sides of the equation by 50:

$a = \frac{0}{50}$

$a = 0$

Therefore, the solution to the problem is $a = 0$.

First we will move terms so that -b remains remains on the left side of the equation.

We'll move 8 to the right-hand side, making sure to retain the plus and minus signs accordingly:

$-b=6-8$

Then we will subtract as follows:

$-b=-2$

Finally, we will divide both sides by -1 (be careful with the plus and minus signs when dividing by a negative):

$\frac{-b}{-1}=\frac{-2}{-1}$

$b=2$

Let's solve the equation $-16 + a = -17$ by isolating the variable $a$.

To isolate $a$, add 16 to both sides of the equation to cancel out the $-16$:

$-16 + a + 16 = -17 + 16$

This simplification results in:

$a = -1$

Thus, the solution to the equation $-16 + a = -17$ is $a = -1$.

If we review the answer choices given, the correct answer is Choice 4, $-1$.

The solution to the problem is $a = -1$.

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

• Step 1: Combine like terms.
• Step 2: Simplify and isolate the variable.
• Step 3: Solve for the variable.

Let's address each step in detail:
Step 1: Combine the like terms on the left side of the equation.
The original equation is: $2 + 4y - 2y = 4$ Combine the terms involving $y$:
$4y - 2y = 2y$ The equation now becomes:
$2 + 2y = 4$ Step 2: Simplify the equation to isolate $2y$.
Subtract 2 from both sides to begin the process of isolating $y$:
$2y = 4 - 2$ Simplify the right side:
$2y = 2$ Step 3: Solve for $y$ by dividing both sides by 2:
$y = \frac{2}{2}$ This simplifies to:
$y = 1$ Thus, the solution to the equation is: $y = 1$.

To solve the equation $x + x = 8$, follow these steps:

• Step 1: Combine like terms. Since the left side of the equation is $x + x$, it can be simplified to $2x$. This gives us the equation $2x = 8$.
• Step 2: Solve for $x$ by isolating it. Divide both sides of the equation by 2 to get $x$.
• Performing the division gives $x = \frac{8}{2}$.
• Step 3: Calculate the result of the division. $\frac{8}{2} = 4$.

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

To solve this problem, we'll follow the procedure of simplifying and solving for $x$:

• Step 1: Simplify both sides of the equation.
• Step 2: Combine like terms and move them to opposite sides to isolate $x$.
• Step 3: Solve for $x$ by performing necessary arithmetic operations.

Now, let's work through each step:

Step 1: Simplify both sides of the equation.
The given equation is $x + 3 - 8x = 4 + 3 - x$.
Combine like terms on each side:
Left side: $x - 8x + 3 = -7x + 3$
Right side: $4 - x + 3 = 7 - x$
So the equation becomes: $-7x + 3 = 7 - x$.

Step 2: Get all terms involving $x$ on one side of the equation.
Add $x$ to both sides to combine the $x$ terms:
$-7x + x + 3 = 7 - x + x$
Simplifies to: $-6x + 3 = 7$

Step 3: Solve for $x$.
Subtract 3 from both sides to isolate terms involving $x$: $-6x + 3 - 3 = 7 - 3$ $-6x = 4$
Now, divide both sides by $-6$ to solve for $x$: $x = \frac{4}{-6} = -\frac{2}{3}$

Therefore, the solution to the problem is $x = -\frac{2}{3}$.

To solve for $x$, let's follow these steps:

• Step 1: Combine like terms on both sides of the equation.
• Step 2: Isolate the $x$ terms on one side.
• Step 3: Solve for $x$.

Let's begin with the left side of the equation:
$-5x + 20 - 3x$ simplifies to $-8x + 20$.

Next, the right side of the equation:
$40 + 2 - 6x$ simplifies to $42 - 6x$.

The equation now is:
$-8x + 20 = 42 - 6x$.

Step 2: Move all terms containing $x$ to one side and constant terms to the other:

First, add $8x$ to both sides to move the $x$ terms together:
$-8x + 8x + 20 = 42 + 2x$
which simplifies to $20 = 42 + 2x$.

Next, subtract $42$ from both sides to get:
$20 - 42 = 2x$
which simplifies to $-22 = 2x$.

Step 3: Solve for $x$ by dividing both sides by 2:
$x = \frac{-22}{2} = -11$.

Therefore, the solution to the problem is $x = -11$.

First, we divide both sections by 8:

$\frac{8(-2-x)}{8}=\frac{16}{8}$

Keep in mind that the 8 in the fraction of the left section is reduced, so the equation we get is:

$-2-x=2$

We move the minus 2 to the right section and maintain the plus and minus signs accordingly:

$-x=2+2$

$-x=4$

We divide both sides by minus 1 and maintain the plus and minus signs accordingly when we divide:

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

$x=-4$

To solve the linear equation $a + 7 + 3a - 15 = 0$, we follow these steps:

• Step 1: Combine like terms.
• Step 2: Simplify the equation.
• Step 3: Solve for $a$.

Let's execute each step:

Step 1: Combine like terms.
We have $1a + 3a = 4a$. The equation becomes:

$4a + 7 - 15 = 0$

Step 2: Simplify the equation.
Combine the constants $7$ and $-15$:

$4a - 8 = 0$

Step 3: Solve for $a$.
Add 8 to both sides to isolate the term with $a$:

$4a = 8$

Divide both sides by 4 to solve for $a$:

$a = \frac{8}{4} = 2$

Therefore, the solution to the equation is $a = 2$.

To solve the linear equation $x + 8 + 3x - 4 = 0$, follow these steps:

• Step 1: Combine like terms.
  Combine the terms involving $x$, specifically $x + 3x = 4x$.
  Combine the constant terms, specifically $8 - 4 = 4$.
  The equation becomes $4x + 4 = 0$.
• Step 2: Isolate the variable $x$.
  Subtract 4 from both sides to get $4x = -4$.
• Step 3: Solve for $x$.
  Divide both sides by 4 to solve for $x$, resulting in $x = -1$.

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

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

• Step 1: Simplify the equation by combining like terms.
• Step 2: Isolate the variable $b$ on one side of the equation.
• Step 3: Solve for the value of $b$.

Now, let's work through these steps:
Step 1: Combine the terms $b$ and $2b$ to simplify the equation:
$b + 2b + 4 = 0$ becomes $3b + 4 = 0$.

Step 2: Isolate the variable $b$ by subtracting 4 from both sides:
$3b + 4 - 4 = 0 - 4$ simplifies to $3b = -4$.

Step 3: Solve for $b$ by dividing both sides by 3:
$b = \frac{-4}{3}$.

The solution to the problem is $b = -1\frac{1}{3}$.

Therefore, choice 4 is the correct option: $-1\frac{1}{3}$.

We will rearrange the equation so that x remains on the left side and we will move similar elements to the right side.

Remember that when we move a positive number, it will become a negative number, so we will get:

$x=3-5$

$x=-2$

To solve the equation $-3 - x = 4$, let's follow these steps:

• Start by isolating $x$. We will first eliminate the $-x$ term from the left side by adding $x$ to both sides of the equation. This gives us:

$-3 = 4 + x$

• Now, subtract $4$ from both sides to solve for $x$. This step ensures $x$ is isolated:

$-3 - 4 = x$

• Calculate the result on the left side:

$-7 = x$

Hence, the solution to the given equation is $x = -7$.

Reviewing the choices, the correct choice is , which is $-7$.