Solve the equations and check your answer in the case:
`7-2(5-3x)=4(x-3)+5`

Options

A. x = -3
B. x = -2
C. x = -4
D. x = -5

Answer

To solve the equation \( 7 - 2(5 - 3x) = 4(x - 3) + 5 \), we will follow these steps:

### Step 1: Expand both sides of the equation
Start by distributing the terms inside the parentheses.

**Left Side:**
\[ 7 - 2(5 - 3x) = 7 - 10 + 6x \]
So, the left side simplifies to:
\[ 7 - 10 + 6x = -3 + 6x \]

**Right Side:**
\[ 4(x - 3) + 5 = 4x - 12 + 5 \]
So, the right side simplifies to:
\[ 4x - 12 + 5 = 4x - 7 \]

Now, we rewrite the equation:
\[ -3 + 6x = 4x - 7 \]

### Step 2: Move all terms involving \(x\) to one side and constant terms to the other side
Subtract \(4x\) from both sides:
\[ -3 + 6x - 4x = -7 \]
This simplifies to:
\[ -3 + 2x = -7 \]

Next, add \(3\) to both sides:
\[ 2x = -7 + 3 \]
This simplifies to:
\[ 2x = -4 \]

### Step 3: Solve for \(x\)
Now, divide both sides by \(2\):
\[ x = \frac{-4}{2} \]
This gives:
\[ x = -2 \]

### Step 4: Check the solution
To verify, substitute \(x = -2\) back into the original equation.

**Left Side:**
\[ 7 - 2(5 - 3(-2)) = 7 - 2(5 + 6) = 7 - 2(11) = 7 - 22 = -15 \]

**Right Side:**
\[ 4(-2 - 3) + 5 = 4(-5) + 5 = -20 + 5 = -15 \]

Since both sides are equal:
\[ -15 = -15 \]

Thus, the solution is verified.

### Final Answer:
The value of \(x\) is \(-2\).

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