Solving Equations by using Addition/ Subtraction: Simplifying expressions

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 $3x + 5 = 2x + 20$, 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 $x = 2$.

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 $-8$.

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 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 $4$.