Solve Linear Equation: -4(6-x)+(3x+5)=14 Step-by-Step

To solve this problem, we'll follow these steps:

• Step 1: Apply the distributive property to expand the expression.
• Step 2: Simplify both sides to isolate the variable.
• Step 3: Divide to solve for the variable.

Now, let's work through each step:

Step 1: Apply the distributive property
The given equation is $-4(6-x)+(3x+5)=14$.
First, distribute $-4$:
$-4 \times 6 + -4 \times -x = -24 + 4x$.
Insert this into the equation:
$-24 + 4x + 3x + 5 = 14$.

Step 2: Simplify the equation
Combine like terms (the $x$ terms and constants):
$4x + 3x = 7x$.
$-24 + 5 = -19$.
So, the equation becomes:
$7x - 19 = 14$.

Step 3: Solve for $x$
Add 19 to both sides to isolate the $x$-term:
$7x - 19 + 19 = 14 + 19$.
$7x = 33$.
Divide both sides by 7:
$x = \frac{33}{7}$.
Simplifying this gives $x = 4\frac{5}{7}$.

Therefore, the solution to the problem is $x = 4\frac{5}{7}$.