To solve the expression [tex]\(2(5x + 4) - 5(4x - 3)\)[/tex], we will distribute the constants through the parentheses and then combine like terms. Here is a detailed, step-by-step explanation:
1. Distribute the constants through the parentheses:
[tex]\[
2(5x + 4) - 5(4x - 3)
\][/tex]
Start by distributing the 2:
[tex]\[
2 \cdot 5x + 2 \cdot 4 = 10x + 8
\][/tex]
Next, distribute the -5:
[tex]\[
-5 \cdot 4x + -5 \cdot (-3) = -20x + 15
\][/tex]
2. Combine the distributed terms:
[tex]\[
10x + 8 - 20x + 15
\][/tex]
3. Group the like terms:
Combine the [tex]\(x\)[/tex]-terms:
[tex]\[
10x - 20x = -10x
\][/tex]
And then combine the constant terms:
[tex]\[
8 + 15 = 23
\][/tex]
4. Combine the results of the like terms:
[tex]\[
-10x + 23
\][/tex]
So, the expression [tex]\(2(5x + 4) - 5(4x - 3)\)[/tex] simplifies to:
[tex]\[
\boxed{-10}x + \boxed{23}
\][/tex]
Therefore, the variables to fill in the blanks are:
[tex]\[
-10 \quad \text{and} \quad 23.
\][/tex]
