Solve (1/2x+3)-(4x+7)=1: Linear Equation with Fractions

To solve the equation $(\frac{1}{2}x + 3) - (4x + 7) = 1$, follow these steps:

• Simplify the Left Side:

Begin by distributing the negative sign to the terms in the parentheses on the left-hand side: $(\frac{1}{2}x + 3) - 4x - 7 = 1$

Combine like terms: $\frac{1}{2}x - 4x + 3 - 7 = 1$

This simplifies to: $-\frac{7}{2}x - 4 = 1$

• Isolate the Variable $x$:

Add 4 to both sides to isolate the term involving $x$: $-\frac{7}{2}x - 4 + 4 = 1 + 4$

Resulting in: $-\frac{7}{2}x = 5$

• Solve for $x$:

Multiply both sides by the reciprocal of $-\frac{7}{2}$, which is $-\frac{2}{7}$, to solve for $x$: $x = 5 \times \left(-\frac{2}{7}\right)$

Calculate the product: $x = -\frac{10}{7}$

Convert to a mixed number: $x = -1\frac{3}{7}$

Therefore, the solution to the problem is $x = -1\frac{3}{7}$.

The correct choice from the options given is choice $-1\frac{3}{7}$ (Choice 3).