If `3 ( 5x - 7) - 4 ( 8x - 13) = 2 ( 9x - 11) - 17,` then the value of `( 7x - 5)/(11 x - 9) ` is

Options

A. `- (14)/(31)`
B. `- (9)/(13)`
C. `(9)/(13)`
D. `(14)/(31)`

Answer

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

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

Left side:
\[ 3(5x - 7) = 15x - 21 \]
\[ -4(8x - 13) = -32x + 52 \]
Combining these gives:
\[ 15x - 21 - 32x + 52 = -17x + 31 \]

Right side:
\[ 2(9x - 11) = 18x - 22 \]
So, we have:
\[ 18x - 22 - 17 = 18x - 39 \]

Now, the equation is:
\[ -17x + 31 = 18x - 39 \]

### Step 2: Move all terms involving \(x\) to one side
Add \(17x\) to both sides:
\[ 31 = 35x - 39 \]

### Step 3: Move constant terms to the other side
Add \(39\) to both sides:
\[ 31 + 39 = 35x \]
\[ 70 = 35x \]

### Step 4: Solve for \(x\)
Divide both sides by \(35\):
\[ x = \frac{70}{35} = 2 \]

### Step 5: Substitute \(x\) into \((7x - 5)/(11x - 9)\)
Now substitute \(x = 2\) into the expression \((7x - 5)/(11x - 9)\):
\[ 7(2) - 5 = 14 - 5 = 9 \]
\[ 11(2) - 9 = 22 - 9 = 13 \]
So, we have:
\[ \frac{9}{13} \]

### Final Answer
The value of \(\frac{7x - 5}{11x - 9}\) is \(\frac{9}{13}\).

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