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 $x = 15$.