Let's solve the given equation step by step.

The equation is:

$3(4x - 7) = 10(x + 5)$

Step 1: Distribute the constants on both sides.

On the left side, distribute $3$ across $4x - 7$:

$3 \times 4x - 3 \times 7 = 12x - 21$

On the right side, distribute $10$ across $x + 5$:

$10 \times x + 10 \times 5 = 10x + 50$

Now, the equation is:

$12x - 21 = 10x + 50$

Step 2: Move the $x$ terms to one side.

Subtract $10x$ from both sides:

$12x - 10x - 21 = 50$

Simplifying:

$2x - 21 = 50$

Step 3: Move the constant terms to the other side.

Add $21$ to both sides:

$2x = 50 + 21$

Simplifying:

$2x = 71$

Step 4: Solve for $x$.

Divide both sides by $2$:

$x = \frac{71}{2}$

So, the solution is:

$x = 35.5$

If you have any further questions or need more details, feel free to ask!

Related Questions:

1. How do you solve equations with fractions on both sides?
2. What are some common mistakes when distributing constants in equations?
3. How can you verify the solution of an equation?
4. What steps are needed if the equation involves decimals instead of integers?
5. How do you solve for $x$ if the equation has variables on both sides with different coefficients?

Tip:

Always double-check your distribution and combining like terms to avoid simple mistakes when solving equations!