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400 + -3t = 180 + 5t

What does t equal?

11 answers

To solve the equation \( 400 + -3t = 180 + 5t \), we can follow these steps:

  1. Combine like terms by moving all terms involving \( t \) to one side and the constant terms to the other side. First, let's add \( 3t \) to both sides:

\[ 400 = 180 + 5t + 3t \]

This simplifies to:

\[ 400 = 180 + 8t \]

  1. Next, subtract \( 180 \) from both sides:

\[ 400 - 180 = 8t \]

This gives us:

\[ 220 = 8t \]

  1. Now, divide both sides by \( 8 \) to solve for \( t \):

\[ t = \frac{220}{8} = 27.5 \]

Thus, the solution is:

\[ t = 27.5 \]

400 + (-3 • 27.5)

To calculate \( 400 + (-3 \cdot 27.5) \):

  1. First, calculate \( -3 \cdot 27.5 \): \[ -3 \cdot 27.5 = -82.5 \]

  2. Now, add this result to 400: \[ 400 + (-82.5) = 400 - 82.5 = 317.5 \]

So, \( 400 + (-3 \cdot 27.5) = 317.5 \).

180 + 5 • 27.5

To calculate \( 180 + 5 \cdot 27.5 \):

  1. First, calculate \( 5 \cdot 27.5 \): \[ 5 \cdot 27.5 = 137.5 \]

  2. Now, add this result to 180: \[ 180 + 137.5 = 317.5 \]

So, \( 180 + 5 \cdot 27.5 = 317.5 \).

-8 + 3x = -2 + 2x
What does x equal?

To solve the equation \( -8 + 3x = -2 + 2x \), follow these steps:

  1. First, let's isolate the terms involving \( x \) on one side of the equation. We can subtract \( 2x \) from both sides:

\[ -8 + 3x - 2x = -2 + 2x - 2x \]

This simplifies to:

\[ -8 + x = -2 \]

  1. Next, add \( 8 \) to both sides to isolate \( x \):

\[ x = -2 + 8 \]

This gives us:

\[ x = 6 \]

Therefore, the solution is:

\[ x = 6 \]

-8 + 3 + 6

To calculate \(-8 + 3 + 6\):

  1. First, add \(-8\) and \(3\): \[ -8 + 3 = -5 \]

  2. Next, add \(-5\) and \(6\): \[ -5 + 6 = 1 \]

So, \(-8 + 3 + 6 = 1\).

-8 + 3x = -2 + 2x
(X equals 6)

Let's confirm that \( x = 6 \) is a solution to the equation \( -8 + 3x = -2 + 2x \) by substituting \( x = 6 \) into the equation.

  1. Substitute \( x = 6 \) into the left side of the equation: \[ -8 + 3(6) = -8 + 18 = 10 \]

  2. Now substitute \( x = 6 \) into the right side of the equation: \[ -2 + 2(6) = -2 + 12 = 10 \]

Since both sides are equal (10 = 10), it confirms that \( x = 6 \) is indeed a solution to the equation \( -8 + 3x = -2 + 2x \).

If you have any further questions or need additional help, feel free to ask!