Explicație pas cu pas:
[tex] |2x + 3| + x = 5[/tex]
[tex]2x + 3 = 0 \\ 2x = - 3 = > x = - \frac{3}{2}[/tex]
1.
[tex]x < - \frac{3}{2} = > |2x + 3| = - 2x - 3[/tex]
[tex] - 2x - 3 + x = 5 \\ - x = 5 + 3 \\ - x = 8 = > x = - 8\in\left(- \infty ; - \frac{3}{2} \right)[/tex]
2.
[tex]x \geqslant - \frac{3}{2} = > |2x + 3| = 2x + 3[/tex]
[tex]2x + 3 + x = 5 \\ 3x = 5 - 3 \\ 3x = 2 = > x = \frac{2}{3}\in \left[ - \frac{3}{2} ; + \infty \right)[/tex]
[tex]\Rightarrow S = \{ - 8; \frac{2}{3} \} \\ [/tex]
