Question

Solve \(7 s=-56\)

Short answer

The solution is s = -8.

Step-by-step solution

Understand the Equation

The given equation is a basic linear equation where the variable to solve for is 's'. The equation is: \[ 7s = -56 \]

Isolate the Variable 's'

To solve for 's', we need to isolate it on one side of the equation. We do this by dividing both sides of the equation by the coefficient of 's', which is 7.

Divide Both Sides by 7

Perform the division: \[ s = \frac{-56}{7} \]

Simplify the Division

Now, simplify the division: \[ s = -8 \]

Verify the Solution

To ensure the solution is correct, substitute '-8' back into the original equation: \[ 7(-8) = -56 \]Since both sides of the equation match, the solution is verified.

Key concepts

Isolating Variables

Isolating the variable is crucial in solving linear equations. When we face an equation like \[7s = -56\], our goal is to get 's' by itself on one side of the equation. We do this by performing operations that will cancel out the coefficient next to 's'. In this case, we need to eliminate the 7 attached to 's'. To achieve this, we divide both sides of the equation by 7. This step might look like:\[ \frac{7s}{7} = \frac{-56}{7} \]
Division helps to separate 's' from its coefficient, giving us:\[ s = -8 \]
The trick is to remember that whatever operation we do to one side of the equation, we must also do to the other side to keep the equation balanced.

Simplifying Division

Simplifying the division is another key step. After dividing both sides by 7, we need to simplify the resulting fraction, \[ \frac{-56}{7} \].
Let's break down the division process:

• Identify the numerator (-56) and the denominator (7).
• Determine if the fraction can be simplified.
• Perform the division: \[ -56 \div 7 = -8 \]

The result is that \[ s = -8 \]. Simplification makes our answer clear and concise. Always review if the division is carried out correctly to avoid common pitfalls.

Verifying Solutions

Verifying the solution is the final check to ensure our answer is correct. Take the value of 's' that we found, which is -8, and substitute it back into the original equation: \[ 7s = -56 \]
Replace 's' with -8: \[ 7(-8) = -56 \]
Calculate the left-hand side:

• \[ 7 \times -8 = -56 \]

Both sides of the equation match, confirming that \[ s = -8 \] is indeed the correct solution. This step ensures that no mistakes were made during the isolation and simplification processes.