After distributing, combine like terms (the x-terms together and the constants together) on each side before trying to solve the equation.

Once each side is simplified, move all the x-terms to one side of the equation and all the constant numbers to the other side. What operation will undo an extra x-term or constant?

In Desmos, enter the left side as y = 4(2x + 5) - 3x and the right side as y = 7(x - 2) + 10. You will see two lines on the graph.

Tap or click on the point where the two lines intersect. The x-coordinate of this intersection is the solution to the equation $4(2x + 5) - 3x = 7(x - 2) + 10$.

Start by removing the parentheses using the distributive property.

• Left side: $4(2x + 5) - 3x$
  • Distribute $4$: $4 \cdot 2x = 8x$ and $4 \cdot 5 = 20$, so this becomes $8x + 20 - 3x$.
• Right side: $7(x - 2) + 10$
  • Distribute $7$: $7 \cdot x = 7x$ and $7 \cdot (-2) = -14$, so this becomes $7x - 14 + 10$.

Now simplify each side by combining like terms.

• Left side: $8x + 20 - 3x$
  • Combine $8x$ and $-3x$ to get $5x$, so the left side is $5x + 20$.
• Right side: $7x - 14 + 10$
  • Combine $-14$ and $10$ to get $-4$, so the right side is $7x - 4$.

Now the equation is:

Move all the x-terms to one side and the constant terms to the other.

• Subtract $5x$ from both sides:

• Now add $4$ to both sides to move constants away from the x-term:

Now isolate $x$ by dividing both sides by $2$:

So the value of $x$ is $12$. You can check by substituting $x=12$ back into the original equation to confirm both sides are equal.