solve `3(5x-7)-2(9x-11)=4(8x-13)-17`

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

To solve the equation \(3(5x-7)-2(9x-11)=4(8x-13)-17\), we will follow these steps:

### Step 1: Expand the brackets
We start by distributing the numbers outside the brackets to the terms inside the brackets.

\[ 3(5x - 7) = 15x - 21 \]
\[ -2(9x - 11) = -18x + 22 \]
\[ 4(8x - 13) = 32x - 52 \]

Now, substituting these back into the equation, we have:

\[ 15x - 21 - 18x + 22 = 32x - 52 - 17 \]

### Step 2: Combine like terms on both sides
Now, we will combine the like terms on both sides of the equation.

On the left side:
\[ (15x - 18x) + (-21 + 22) = -3x + 1 \]

On the right side:
\[ 32x - (52 + 17) = 32x - 69 \]

So the equation now looks like:
\[ -3x + 1 = 32x - 69 \]

### Step 3: Move all terms involving \(x\) to one side
To isolate \(x\), we can add \(3x\) to both sides:

\[ 1 = 32x + 3x - 69 \]
\[ 1 = 35x - 69 \]

### Step 4: Move constant terms to the other side
Next, we add \(69\) to both sides:

\[ 1 + 69 = 35x \]
\[ 70 = 35x \]

### Step 5: Solve for \(x\)
Finally, we divide both sides by \(35\):

\[ x = \frac{70}{35} \]
\[ x = 2 \]

### Final Answer
Thus, the solution to the equation is:
\[ \boxed{2} \]

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