Answer :
Sure, let's solve the equation step-by-step:
[tex]\[ -4x - 4 = -4(x + 2) \][/tex]
First, we need to distribute the [tex]\(-4\)[/tex] on the right side of the equation:
[tex]\[ -4x - 4 = -4 \cdot x - 4 \cdot 2 \][/tex]
[tex]\[ -4x - 4 = -4x - 8 \][/tex]
Next, we observe that both sides of the equation contain [tex]\(-4x\)[/tex]. To simplify, let's add [tex]\(4x\)[/tex] to both sides of the equation:
[tex]\[ -4x - 4 + 4x = -4x - 8 + 4x \][/tex]
[tex]\[ -4 = -8 \][/tex]
At this point, we reach a contradiction because [tex]\(-4\)[/tex] does not equal [tex]\(-8\)[/tex]. This indicates that there is no value of [tex]\(x\)[/tex] that satisfies the original equation.
Therefore, the equation has:
[tex]\[ \text{No solution} \][/tex]
The correct answer is: No solution.
[tex]\[ -4x - 4 = -4(x + 2) \][/tex]
First, we need to distribute the [tex]\(-4\)[/tex] on the right side of the equation:
[tex]\[ -4x - 4 = -4 \cdot x - 4 \cdot 2 \][/tex]
[tex]\[ -4x - 4 = -4x - 8 \][/tex]
Next, we observe that both sides of the equation contain [tex]\(-4x\)[/tex]. To simplify, let's add [tex]\(4x\)[/tex] to both sides of the equation:
[tex]\[ -4x - 4 + 4x = -4x - 8 + 4x \][/tex]
[tex]\[ -4 = -8 \][/tex]
At this point, we reach a contradiction because [tex]\(-4\)[/tex] does not equal [tex]\(-8\)[/tex]. This indicates that there is no value of [tex]\(x\)[/tex] that satisfies the original equation.
Therefore, the equation has:
[tex]\[ \text{No solution} \][/tex]
The correct answer is: No solution.
