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Which statement is true about this equation?

[tex]\[ -4(2p + 5) + 8p = -11 \][/tex]

A. The equation has one solution, [tex]\( p = 2 \)[/tex].

B. The equation has one solution, [tex]\( p = -2 \)[/tex].

C. The equation has no solution.

D. The equation has infinitely many solutions.

Sagot :

GinnyAnswer
To analyze the given equation [tex]\( -4(2p + 5) + 8p = -11 \)[/tex] and determine which statement is true, we'll go through the following steps:

### Step 1: Distribute the Constant
First, distribute the [tex]\(-4\)[/tex] across the terms inside the parentheses.
[tex]\[ -4(2p + 5) + 8p = -11 \][/tex]
[tex]\[ -8p - 20 + 8p = -11 \][/tex]

### Step 2: Combine Like Terms
Combine the [tex]\( -8p \)[/tex] and [tex]\( +8p \)[/tex] on the left-hand side of the equation.
[tex]\[ -8p + 8p - 20 = -11 \][/tex]
[tex]\[ 0 - 20 = -11 \][/tex]
[tex]\[ -20 = -11 \][/tex]

### Conclusion
After simplifying, we obtain [tex]\( -20 = -11 \)[/tex], which is a false statement. This indicates that no values of [tex]\( p \)[/tex] can satisfy the equation because [tex]\(-20\)[/tex] is not equal to [tex]\(-11\)[/tex].

### Final Answer
Based on these steps, we see that the equation has no solution. Therefore, the correct choice is:

C. The equation has no solution.
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