Question

Solve the equation. Write a justification for each step. 8 − 5s = 1

Answer 1

The equation 8 - 5s = 1 is solved by isolating the variable and dividing by the coefficient, yielding s = 1.4. The solution is verified by substituting it back into the original equation and confirming the equality holds true.

Step-by-step explanation:

To solve the equation 8 − 5s = 1, we will apply basic algebraic principles.

1. Isolate the variable term: We want to get the term with the variable 's' by itself. To do this, we subtract 8 from both sides of the equation to maintain equality.
2. 8 − 5s − 8 = 1 − 8
3. This simplifies to −5s = −7.
4. Divide by the coefficient of s: To isolate 's' completely, we divide both sides of the equation by -5, the coefficient of 's'.
5. (-5s) / -5 = (-7) / -5
6. This gives us s = 7/5 or s = 1.4.

Verifying the Solution

To verify that our solution makes sense, we substitute s = 1.4 back into the original equation:

8 − 5(1.4) = 1

After performing the multiplication and subtraction, we find that the left side equals 1, which is the same as the right side, confirming that our solution is correct.