Sure, here are the solutions for Bài 5:

a) \(|4 + 2x| = -4x\)

This equation doesn't have a solution because the absolute value cannot be negative. So, there is no solution for (a).

b) \(|3x - 1| + 2 = x\)

Consider two cases:

**Case 1:** \(3x - 1 \geq 0\) (implies \(3x \geq 1\) or \(x \geq \frac{1}{3}\))

\[
3x - 1 + 2 = x \implies 2x + 1 = x \implies x = -1
\]

This does not satisfy the condition \(x \geq \frac{1}{3}\). So, no solution in this case.

**Case 2:** \(3x - 1 < 0\) (implies \(3x < 1\) or \(x < \frac{1}{3}\))

\[
-(3x - 1) + 2 = x \implies -3x + 1 + 2 = x \implies -4x + 3 = x \implies 5x = 3 \implies x = \frac{3}{5}
\]

This does not satisfy the condition \(x < \frac{1}{3}\). So, no solution in this case.

Therefore, no solution for (b).

c) \(|x + 15| + 1 = 3x\)

Consider two cases:

**Case 1:** \(x + 15 \geq 0\) (implies \(x \geq -15\))

\[
x + 15 + 1 = 3x \implies x + 16 = 3x \implies 2x = 16 \implies x = 8
\]

This satisfies \(x \geq -15\).

**Case 2:** \(x + 15 < 0\) (implies \(x < -15\))

\[
-(x + 15) + 1 = 3x \implies -x - 15 + 1 = 3x \implies -x - 14 = 3x \implies -4x = 14 \implies x = -\frac{14}{4} = -\frac{7}{2}
\]

This does not satisfy \(x < -15\).

So, \(x = 8\).

d) \(|7 - x| = 5x + 1\)

Consider two cases:

**Case 1:** \(7 - x \geq 0\) (implies \(x \leq 7\))

\[
7 - x = 5x + 1 \implies 7 = 6x + 1 \implies 6 = 6x \implies x = 1
\]

This satisfies \(x \leq 7\).

**Case 2:** \(7 - x < 0\) (implies \(x > 7\))

\[
-(7 - x) = 5x + 1 \implies -7 + x = 5x + 1 \implies x - 5x = 1 + 7 \implies -4x = 8 \implies x = -2
\]

This does not satisfy \(x > 7\).

So, \(x = 1\).

e) \(|5x| = x - 12\)

Consider two cases:

**Case 1:** \(5x \geq 0\) (implies \(x \geq 0.12\))

\[
5x = x - 12 \implies 4x = -12 \implies x = -3
\]

This does not satisfy \(x \geq 0.12\).

**Case 2:** \(5x < 0\) (implies \(x < 0.12\))

\[
-5x = x - 12 \implies -6x = -12 \implies x = 2
\]

This satisfies \(x < 0.12\).

So, \(x = 2\).

f) \(|2x - 3| + x = 21\)

Consider two cases:

**Case 1:** \(2x - 3 \geq 0\) (implies \(x \geq 1.5\))

\[
2x - 3 + x = 21 \implies 3x - 3 = 21 \implies 3x = 24 \implies x = 8
\]

This satisfies \(x \geq 1.5\).

**Case 2:** \(2x - 3 < 0\) (implies \(x < 1.5\))

\[
-(2x - 3) + x = 21 \implies -2x + 3 + x = 21 \implies -x + 3 = 21 \implies -x = 18 \implies x = -18
\]

This does not satisfy \(x < 1.5\).

So, \(x = 8\).