Simplify the expression: 4(x - 2) + 3(x + 1).

To simplify the expression 4(x - 2) + 3(x + 1), you can begin by distributing the constants 4 and 3 to each term inside the parentheses.

First, apply the distributive property:

• Multiply 4 by each term in (x - 2):

• 4 * x = 4x

• 4 * -2 = -8

So, 4(x - 2) becomes 4x - 8.

Next, do the same for 3(x + 1):

• 3 * x = 3x

• 3 * 1 = 3

Thus, 3(x + 1) becomes 3x + 3.

Now, you can combine these results:

4(x - 2) + 3(x + 1) becomes (4x - 8) + (3x + 3).

Combine like terms:

• The x terms: 4x + 3x = 7x.

• The constant terms: -8 + 3 = -5.

Putting it all together, you have:

7x - 5.

This shows that the simplified expression from the original question is indeed