(2a+3)-(4a-8)=7 Value Of A

2 min read Jun 16, 2024

Solving for 'a' in the Equation (2a + 3) - (4a - 8) = 7

This article will guide you through the steps to solve the equation (2a + 3) - (4a - 8) = 7 to find the value of 'a'.

Understanding the Equation

The equation involves simplifying expressions with variables and constants. The goal is to isolate 'a' on one side of the equation.

Solving for 'a'

Distribute the negative sign:
- The negative sign before the parentheses means we multiply each term inside the parentheses by -1.
- This gives us: 2a + 3 - 4a + 8 = 7
Combine like terms:
- Combine the 'a' terms: 2a - 4a = -2a
- Combine the constant terms: 3 + 8 = 11
- Now the equation becomes: -2a + 11 = 7
Isolate the 'a' term:
- Subtract 11 from both sides of the equation: -2a + 11 - 11 = 7 - 11
- This simplifies to: -2a = -4
Solve for 'a':
- Divide both sides of the equation by -2: -2a / -2 = -4 / -2
- This gives us the final solution: a = 2

Verification

We can verify our answer by substituting 'a = 2' back into the original equation:

(2 * 2 + 3) - (4 * 2 - 8) = 7 (4 + 3) - (8 - 8) = 7 7 - 0 = 7 7 = 7

This verifies that a = 2 is the correct solution to the equation.

Conclusion

By applying the principles of simplifying expressions and solving for variables, we successfully determined the value of 'a' to be 2 in the equation (2a + 3) - (4a - 8) = 7.