Sure, let's solve the equation step by step. We start with the given equation:
[tex]\[ 20 = 10x - 6(2x + 5) \][/tex]
1. First, distribute [tex]\(-6\)[/tex] inside the parentheses:
[tex]\[ 20 = 10x - 6 \cdot 2x - 6 \cdot 5 \][/tex]
[tex]\[ 20 = 10x - 12x - 30 \][/tex]
2. Combine like terms on the right side of the equation:
[tex]\[ 20 = (10x - 12x) - 30 \][/tex]
[tex]\[ 20 = -2x - 30 \][/tex]
3. Add 30 to both sides of the equation to isolate the term containing [tex]\(x\)[/tex]:
[tex]\[ 20 + 30 = -2x - 30 + 30 \][/tex]
[tex]\[ 50 = -2x \][/tex]
4. Divide both sides by [tex]\(-2\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{50}{-2} \][/tex]
[tex]\[ x = -25 \][/tex]
So, the value of [tex]\(x\)[/tex] that satisfies the equation is:
[tex]\[ x = -25 \][/tex]
This is the solution to the equation [tex]\(20 = 10x - 6(2x + 5)\)[/tex].
