Solving an Equation by Multiplication/ Division: Solving an equation using all techniques

To solve the equation $4y - 7 + 6y = 3 - 10y$, follow these steps:

• Step 1: Combine like terms on both sides of the equation.

The left side simplifies by combining the $y$-terms:
$4y + 6y - 7 = 10y - 7$.

On the right side, there is one $y$-term, but we can leave it for the next steps.

• Step 2: Isolate the $y$-terms.

Add $10y$ to both sides to move all $y$-terms to the left side:

$10y - 7 + 10y = 3$

Simplifying the left side, we get:

$20y - 7 = 3$

• Step 3: Isolate $y$.

Add $7$ to both sides to eliminate the constant term on the left:

$20y = 3 + 7$

$20y = 10$

Divide both sides by $20$ to solve for $y$:

$y = \frac{10}{20}$

$y = \frac{1}{2}$

Therefore, the solution to the problem is $y = \frac{1}{2}$.