To solve the equation
[tex]\[ 5(x + 2) + 4 = 8x - 1 - 3(x - 5) \][/tex]
we need to follow several algebraic steps:
1. Expand the parentheses on both sides:
Left side:
[tex]\[ 5(x + 2) + 4 \][/tex]
Distribute the [tex]\(5\)[/tex] inside the parentheses:
[tex]\[ 5x + 10 + 4 \][/tex]
Combine like terms:
[tex]\[ 5x + 14 \][/tex]
Right side:
[tex]\[ 8x - 1 - 3(x - 5) \][/tex]
First, distribute the [tex]\(-3\)[/tex] inside the parentheses:
[tex]\[ 8x - 1 - 3x + 15 \][/tex]
Combine like terms:
[tex]\[ 5x + 14 \][/tex]
2. Rewrite the equation with the simplified expressions:
[tex]\[ 5x + 14 = 5x + 14 \][/tex]
3. Analyze the simplified equation:
The equation simplifies to:
[tex]\[ 5x + 14 = 5x + 14 \][/tex]
This simplified form essentially states that both sides of the equation are always equal, regardless of the value of [tex]\(x\)[/tex].
4. Conclusion:
Since the simplified equation is always true for all values of [tex]\(x\)[/tex], it indicates that there is no restriction on [tex]\(x\)[/tex]. Therefore, the equation holds true for all real numbers.
So, the correct answer is:
[tex]\[ \text{All real numbers are solutions.} \][/tex]
