Final answer:
To solve the equation 4 · (1-3/4x) + 7 = 10, distribute the 4, combine like terms, and then isolate x by dividing both sides by -3, yielding x = 1/3.
Step-by-step explanation:
To solve the equation 4 · (1-3/4x) + 7 = 10, we follow a sequence of algebraic steps:
- Start by distributing the 4 into the parenthesis: 4 · 1 - 4 · (3/4)x + 7 = 10.
- This simplifies to 4 - 3x + 7 = 10.
- Combine like terms: 11 - 3x = 10.
- Then subtract 11 from both sides: -3x = -1.
- Finally, divide both sides by -3 to solve for x: x = 1/3.
After a series of algebraic manipulations, we find the value of x to be 1/3.
Always remember to eliminate terms wherever possible to simplify the algebra, and check the answer to see if it is reasonable.