If `(4x + 5): (3x + 11)` = `13 : 17`, find the value of x.

Answer

To solve the equation \((4x + 5) : (3x + 11) = 13 : 17\), we will follow these steps:

### Step 1: Set up the equation
We can express the ratio as a fraction:
\[ \frac{4x + 5}{3x + 11} = \frac{13}{17} \]

### Step 2: Cross multiply
To eliminate the fractions, we cross multiply:
\[ 17(4x + 5) = 13(3x + 11) \]

### Step 3: Distribute on both sides
Now, we distribute the numbers on both sides:
\[ 68x + 85 = 39x + 143 \]

### Step 4: Move all terms involving \(x\) to one side
Subtract \(39x\) from both sides:
\[ 68x - 39x + 85 = 143 \]
This simplifies to:
\[ 29x + 85 = 143 \]

### Step 5: Move the constant to the other side
Subtract \(85\) from both sides:
\[ 29x = 143 - 85 \]
This simplifies to:
\[ 29x = 58 \]

### Step 6: Solve for \(x\)
Now, divide both sides by \(29\):
\[ x = \frac{58}{29} \]
This simplifies to:
\[ x = 2 \]

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

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