Question

3.
a. -5x - 3x + 2 = -8x + 2
b. -5x - 3x - 4 = -8x + 2
c. -5x - 4x - 2 = -8x + 2

Explanation:

Step1: Combine like terms (left side)

$-5x - 3x + 2 = -8x + 2$
$\implies -8x + 2 = -8x + 2$

Step2: Add $8x$ to both sides

$-8x + 8x + 2 = -8x + 8x + 2$
$\implies 2 = 2$

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Step1: Combine like terms (left side)

$-5x - 3x - 4 = -8x + 2$
$\implies -8x - 4 = -8x + 2$

Step2: Add $8x$ to both sides

$-8x + 8x - 4 = -8x + 8x + 2$
$\implies -4 = 2$

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Step1: Combine like terms (left side)

$-5x - 4x - 2 = -8x + 2$
$\implies -9x - 2 = -8x + 2$

Step2: Add $9x$ to both sides

$-9x + 9x - 2 = -8x + 9x + 2$
$\implies -2 = x + 2$

Step3: Subtract 2 from both sides

$-2 - 2 = x + 2 - 2$
$\implies x = -4$

Answer:

a. All real numbers (the equation is an identity)
b. No solution (the equation is a contradiction)
c. $x = -4$