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Solve the equation.
[tex]\[ 5(x + 2) + 4 = 8x - 1 - 3(x - 5) \][/tex]

A. There are no solutions.
B. [tex]\( x = \frac{10}{3} \)[/tex]
C. [tex]\( x = 0 \)[/tex]
D. All real numbers are solutions.

Sagot :

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]