if `a=2x+3 and b=4x-7`, for what value of x is `3b=5a`?

Answer

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

### Step 1: Substitute the expressions for \(a\) and \(b\) into the equation \(3b = 5a\).

We know:
- \(a = 2x + 3\)
- \(b = 4x - 7\)

Substituting these into the equation gives us:
\[ 3(4x - 7) = 5(2x + 3) \]

### Step 2: Distribute on both sides of the equation.

Now we will distribute the constants on both sides:
\[ 12x - 21 = 10x + 15 \]

### Step 3: Rearrange the equation to isolate \(x\).

Next, we will move all terms involving \(x\) to one side and constant terms to the other side. We can do this by subtracting \(10x\) from both sides:
\[ 12x - 10x - 21 = 15 \]
This simplifies to:
\[ 2x - 21 = 15 \]

### Step 4: Add 21 to both sides of the equation.

Now, we will add 21 to both sides to isolate the term with \(x\):
\[ 2x = 15 + 21 \]
This simplifies to:
\[ 2x = 36 \]

### Step 5: Divide both sides by 2 to solve for \(x\).

Finally, we will divide both sides by 2:
\[ x = \frac{36}{2} \]
This gives us:
\[ x = 18 \]

### Conclusion:
The value of \(x\) for which \(3b = 5a\) is \(x = 18\).

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