Solve the Absolute Value Inequality for x |4x-4(x+1)|=4

$| 4 x - 4 (x + 1) | = 4$

Simplify $| 4 x - 4 (x + 1) |$ .

Simplify each term.

Apply the distributive property.

$| 4 x - 4 x - 4 \cdot 1 | = 4$

Multiply $- 4$ by $1$ .

$| 4 x - 4 x - 4 | = 4$

Simplify by adding terms.

Subtract $4 x$ from $4 x$ .

$| 0 - 4 | = 4$

Subtract $4$ from $0$ .

$| - 4 | = 4$

The absolute value is the distance between a number and zero. The distance between $- 4$ and $0$ is $4$ .

$4 = 4$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx \frac{1}{2}, \frac{3}{5}, 0.9, 1, 1.1, \frac{6}{5}, 1.3, \frac{8}{5}, 1.7, \frac{9}{5}, 3, 3.1, \frac{16}{5}, 3.3, \frac{17}{5}, \frac{7}{2}, \frac{18}{5}, 3.7, \frac{19}{5}, 3.9, 7, 7.1, \frac{36}{5}, 7.3, \frac{37}{5}, \frac{15}{2}, \frac{38}{5}, 7.7, \frac{39}{5}, 7.9, 15, 15.1, 15.3, 15.4, \frac{31}{2}, 15.6, 15.8, 15.9, 31, 31.1, 31.3, 31.5, 31.6, 31.8, 32$

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

$x \approx 0.5, 0.6, 0.9, 1, 1.1, 1.2, 1.3, 1.6, 1.7, 1.8, 3, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 7, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 15, 15.1, 15.3, 15.4, 15.5, 15.6, 15.8, 15.9, 31, 31.1, 31.3, 31.5, 31.6, 31.8, 32$

Mixed Number Form:

$x \approx \frac{1}{2}, \frac{3}{5}, 0.9, 1, 1.1, 1 \frac{1}{5}, 1.3, 1 \frac{3}{5}, 1.7, 1 \frac{4}{5}, 3, 3.1, 3 \frac{1}{5}, 3.3, 3 \frac{2}{5}, 3 \frac{1}{2}, 3 \frac{3}{5}, 3.7, 3 \frac{4}{5}, 3.9, 7, 7.1, 7 \frac{1}{5}, 7.3, 7 \frac{2}{5}, 7 \frac{1}{2}, 7 \frac{3}{5}, 7.7, 7 \frac{4}{5}, 7.9, 15, 15.1, 15.3, 15.4, 15 \frac{1}{2}, 15.6, 15.8, 15.9, 31, 31.1, 31.3, 31.5, 31.6, 31.8, 32$

Solve the Absolute Value Inequality for x |4x-4(x+1)|=4

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