Solve the Linear Equation: 7(x-4)+3=5-4(x+5) Step by Step

Let's solve the given equation step by step:

We start with the equation:

$7(x-4) + 3 = 5 - 4(x+5)$

Step 1: Apply the distributive property to eliminate the parentheses.

The left-hand side becomes:

$7(x-4) = 7x - 28$, so the entire expression on the left is $7x - 28 + 3$.

The right-hand side becomes:

$-4(x+5) = -4x - 20$, so the whole right side is $5 - 4x - 20$.

Step 2: Simplify both sides.

Simplify the left-hand side:

$7x - 28 + 3 = 7x - 25$.

Simplify the right-hand side:

$5 - 4x - 20 = -4x - 15$.

Now the equation reads:

$7x - 25 = -4x - 15$.

Step 3: Rearrange the equation to isolate $x$ terms on one side and constants on the other.

Add $4x$ to both sides:

$7x + 4x - 25 = -4x + 4x - 15$.

This simplifies to:

$11x - 25 = -15$.

Step 4: Solve for $x$.

Add 25 to both sides:

$11x = 10$.

Divide both sides by 11 to solve for $x$:

$x = \frac{10}{11}$.

Thus, the solution to the equation is $x = \frac{10}{11}$.

Considering the given choices, the correct answer is choice 3: $\frac{10}{11}$.