Solve the following equations.Check your result in each case
`(2x+5)/(3x+4)=3`

Answer

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

### Step 1: Eliminate the fraction
To eliminate the fraction, we can multiply both sides of the equation by \(3x + 4\):
\[ 2x + 5 = 3(3x + 4) \]

### Step 2: Distribute on the right side
Now, we will distribute \(3\) on the right side:
\[ 2x + 5 = 9x + 12 \]

### Step 3: Rearrange the equation
Next, we will rearrange the equation to get all terms involving \(x\) on one side and constant terms on the other side. We can subtract \(2x\) from both sides:
\[ 5 = 9x - 2x + 12 \]
This simplifies to:
\[ 5 = 7x + 12 \]

### Step 4: Isolate the variable
Now, we will isolate \(7x\) by subtracting \(12\) from both sides:
\[ 5 - 12 = 7x \]
This simplifies to:
\[ -7 = 7x \]

### Step 5: Solve for \(x\)
Now, divide both sides by \(7\):
\[ x = -1 \]

### Step 6: Check the result
To check our result, we will substitute \(x = -1\) back into the original equation:
\[ \frac{2(-1) + 5}{3(-1) + 4} = \frac{-2 + 5}{-3 + 4} = \frac{3}{1} = 3 \]
Since both sides are equal, our solution is verified.

### Final Answer
The solution to the equation \(\frac{2x + 5}{3x + 4} = 3\) is:
\[ x = -1 \]

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