Question

3. Să se rezolve ecuaţia |2x+3| +x= 5​

Answer 1

Explicație pas cu pas:

$|2x + 3| + x = 5$

$2x + 3 = 0 \\ 2x = - 3 = > x = - \frac{3}{2}$

1.

$x < - \frac{3}{2} = > |2x + 3| = - 2x - 3$

$- 2x - 3 + x = 5 \\ - x = 5 + 3 \\ - x = 8 = > x = - 8\in\left(- \infty ; - \frac{3}{2} \right)$

2.

$x \geqslant - \frac{3}{2} = > |2x + 3| = 2x + 3$

$2x + 3 + x = 5 \\ 3x = 5 - 3 \\ 3x = 2 = > x = \frac{2}{3}\in \left[ - \frac{3}{2} ; + \infty \right)$

$\Rightarrow S = \{ - 8; \frac{2}{3} \}$