Solving Equations by using Addition/ Subtraction: Test if the coefficient is different from 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 $9$.

To solve the equation $5x + 2 = 4x + 10$, we can simplify and solve for $x$ by following these steps:

• First, let's get all terms involving $x$ on one side and the constant terms on the other. We do this by subtracting $4x$ from both sides:

  $5x + 2 - 4x = 4x + 10 - 4x$

  This simplifies to:

  $x + 2 = 10$

• Next, we need to isolate $x$ by subtracting 2 from both sides:

  $x + 2 - 2 = 10 - 2$

  Which simplifies to:

  $x = 8$

Thus, the solution for $x$ is $8$.

The given equation is: $6x-3=7x+5$

Our goal is to solve for $x$. To achieve this, we'll first get all the terms containing $x$ on one side of the equation and constants on the other side.

Step 1: Subtract $6x$ from both sides to get all $x$ terms on one side:

• $6x - 3 - 6x = 7x + 5 - 6x$

This simplifies to:

• $-3 = x + 5$

Step 2: Next, subtract $5$ from both sides to isolate $x$:

• $-3 - 5 = x + 5 - 5$

This simplifies to:

• $-8 = x$

Therefore, the solution for $x$ is $-8$.

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 $x = 15$.

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 $x = 2$.

Start by moving the $7x$ term to the left side by subtracting $7x$ from both sides:
$8x - 7x - 1 = 7x + 5 - 7x$
This simplifies to:
$x - 1 = 5$

Next, add$1$ to both sides to isolate $x$:
$x - 1 + 1 = 5 + 1$
Simplifying this, we get:
$x = 6$.

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 $x = -4$.

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 problem, let's go through the steps:

First, we start with the given equation:

$0.7x + 0.5 = -0.3x$

To isolate $x$, we will first combine all the $x$-terms on one side. We do this by adding $0.3x$ to both sides of the equation:

$0.7x + 0.3x + 0.5 = 0$

This simplifies to:

$1x + 0.5 = 0$ or $x + 0.5 = 0$

Next, we isolate $x$ by subtracting $0.5$ from both sides:

$x = -0.5$

Therefore, the solution to the problem is $x = -0.5$.

To solve the given problem, we'll proceed as follows:

• Step 1: Simplify both sides of the equation.
• Step 2: Check if $x$ can be isolated or analyze if the equation results in contradictions.

Now, let's work through each step:
Step 1: Simplify the left side: $x + 3 - 4x = (1x - 4x) + 3 = -3x + 3$.
Step 2: Simplify the right side: $5x + 6 - 1 - 8x = (5x - 8x) + (6 - 1) = -3x + 5$.

The simplified equation becomes:

$-3x + 3 = -3x + 5$

To solve for $x$, we attempt to isolate $x$. If we add $3x$ to both sides to eliminate the $-3x$ terms, we get:

$3 = 5$

This results in a contradiction, as 3 is not equal to 5, indicating that there is no value of $x$ that can satisfy this equation.

Therefore, the solution to the problem is no solution as indicated by the contradiction.

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, get all terms involving $x$ on one side and constants on the other. Start from:

$4x - 7 = x + 5$

Subtract $x$ from both sides to simplify:

$3x - 7 = 5$

Add 7 to both sides to isolate the terms with$x$:

$3x = 12$

Divide each side by 3 to solve for$x$:

$x = 4$

Thus, $x$ is $4$.

To solve the equation $4a + 5 - 24 + a = -2a$, follow these steps:

• Step 1: Start by combining like terms on the left side of the equation:

$4a + a + 5 - 24 = -2a$

This simplifies to:

$5a - 19 = -2a$

• Step 2: Move all terms involving $a$ to one side of the equation and constant terms to the other side:

Add $2a$ to both sides to collect all terms with $a$:

$5a + 2a = 19$

This simplifies to:

$7a = 19$

• Step 3: Solve for $a$ by dividing both sides by 7:

$a = \frac{19}{7}$

Thus, the value of $a$ is $\frac{19}{7}$, which can be written as a mixed number:

$a = 2\frac{5}{7}$.

Upon verifying with the given choices, the correct answer is choice 1: $2\frac{5}{7}$.

To solve the problem, we will use the following steps:

• Step 1: Simplify the equation by combining like terms.
• Step 2: Isolate the variable $m$ using algebraic methods.
• Step 3: Solve for $m$ and verify the solution.

Let's begin:

Step 1: Simplify the equation $m + 3m - 17m + 6 = -20$.
Combine the coefficients of $m$:

$(1 + 3 - 17)m + 6 = -20$

This simplifies to:

$-13m + 6 = -20$

Step 2: Isolate $m$.
Subtract 6 from both sides:

$-13m + 6 - 6 = -20 - 6$

Simplifies to:

$-13m = -26$

Step 3: Solve for $m$ by dividing both sides by -13:

$m = \frac{-26}{-13}$

The division simplifies to:

$m = 2$

Therefore, the solution to the problem is $m = 2$, which corresponds to choice 2 in the given options.

It's important to remember that when we have regular numbers and unknowns, we cannot add or subtract them directly.

Let's collect like terms:

5b+2b-7+14=0

7b+7 = 0

Let's move terms

7b = -7

Let's divide by 7

b=-1

And that's the solution!

To solve the equation $14x + 3 = 17$, we need to find the value of $x$ that satisfies the equation.

Step 1: Isolate the term containing $x$ by subtracting 3 from both sides of the equation:

$14x + 3 - 3 = 17 - 3$
This simplifies to:
$14x = 14$

Step 2: Solve for $x$ by dividing both sides by 14:

$x = \frac{14}{14}$
Which simplifies to:
$x = 1$

Therefore, the solution to the equation $14x + 3 = 17$ is $x = 1$.

We begin by placing parentheses around the two multiplication exercises:

$(20\times y)+(8\times2)-7=14$

We then solve the exercises within the parentheses:

$20y+16-7=14$

We simplify:

$20y+9=14$

We move the sections:

$20y=14-9$

$20y=5$

We divide by 20:

$y=\frac{5}{20}$

$y=\frac{5}{5\times4}$

We simplify:

$y=\frac{1}{4}$

To solve the equation $3x + 4 + 8x - 15 = 0$, we begin by combining the terms that involve $x$ and the constant terms:

Step 1: Combine like terms.
The terms involving $x$ are $3x$ and $8x$. Adding these yields:

The constant terms are $+4$ and $-15$. Combining these gives:

Thus, the equation becomes:

Step 2: Solve for $x$.
To isolate $x$, add 11 to both sides of the equation:

Now, divide both sides by 11:

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

We will solve the equation step by step:

Given equation:
$-3x + 8 = 7x - 12$

• Step 1: Move all $x$-terms to one side by adding $3x$ to both sides.
  $-3x + 3x + 8 = 7x + 3x - 12$
  This simplifies to:
  $8 = 10x - 12$
• Step 2: Move constant terms to the opposite side by adding $12$ to both sides.
  $8 + 12 = 10x - 12 + 12$
  Which simplifies to:
  $20 = 10x$
• Step 3: Solve for $x$ by dividing both sides by $10$.
  $\frac{20}{10} = \frac{10x}{10}$
  This gives us:
  $x = 2$

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

First, we arrange the two sections so that the right side contains the values with the coefficient x and the left side the numbers without the x

Let's remember to maintain the plus and minus signs accordingly when we move terms between the sections.

First, we move a$5x$ to the right section and then the 22 to the left side. We obtain the following equation:

$-8-22=10x-5x$

We subtract both sides accordingly and obtain the following equation:

$-30=5x$

We divide both sections by 5 and obtain:

$-6=x$