Final answer:
To solve the given equation, 5x - 4 = 11, add 4 to both sides, then divide by 5 to isolate x, giving x = 3. The solution in set notation is {3}. Checking by substitution confirms the solution is correct.
Step-by-step explanation:
To solve the equation 5x - 4 = 11 for the variable x, follow these steps:
- Add 4 to both sides of the equation to get 5x by itself on the left side:
5x - 4 + 4 = 11 + 4, which simplifies to 5x = 15. - Divide both sides by 5 to isolate x:
5x/5 = 15/5, which simplifies to x = 3. - Express the solution in set notation: {3}.
The solution to the equation is x = 3, and in set notation, it is expressed as {3}.
It's always a good idea to check your solution by substituting it back into the original equation:
- Substitute x = 3 into the original equation: 5(3) - 4.
- Simplify to confirm the equation holds true: 15 - 4 which equals 11, confirming that x = 3 is the correct solution.