The solutions of the given linear equations are: x = 7, - 13; x = 6, - 7; x = 5, - 9, respectively.
What is a linear equation?
A linear equation is an equation that has on or multiple variables with the highest power of the variable is 1.
Given equations are:
1. |3x + 9| = 30
⇒ ( |3x + 9| )² = (30)²
⇒ 9x² + 54x + 81 = 900
⇒ 9x² + 54x + 81 - 900 = 0
⇒ 9x² + 54x - 819 = 0
⇒ 9(x² + 6x - 91) = 0
⇒ (x² + 6x - 91) = 0
⇒ (x + 13)(x - 7) = 0
⇒ x = 7, - 13
2. |2x+1| = - 13
⇒ (|2x+1|)² = (- 13)²
⇒ 4x² + 4x + 1 = 169
⇒ 4x² + 4x - 168 = 0
⇒ 4(x² + x - 42)= 0
⇒ (x² + x - 42)= 0
⇒(x - 6)(x + 7) = 0
⇒ x = 6, - 7
3. |x + 2| + 4 = 11
⇒ |x + 2| = 7
⇒ (|x + 2|)² = 7²
⇒ x² + 4x + 4 = 49
⇒ x² + 4x - 45 = 0
⇒ (x - 5)(x + 9) = 0
⇒ x = 5, - 9
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