358/HK16. problem / Math - Solved Math Problems

MR-358 / 13. problem

Solve the following equation on the set of real numbers!

$7 - 2 (x + 5) = \frac{x + 6}{4} + \frac{x + 2}{2}$

Source: Magyarország: Unified final exam for high schools - Mathematics - intermediate level - 03.05.2016. - 13..)

Algebra → Exponential equations and inequalities → Exponential equations

7 - 2 (x + 5) = \frac{x + 6}{4} + \frac{x + 2}{2}

7 - 2 (x + 5) = \frac{(x + 6) + 2 (x + 2)}{4}

7 - 2 x - 10 = \frac{x + 6 + 2 x + 4}{4}

- 2 x - 3 = \frac{3 x + 10}{4}

- 2 x - 3 = \frac{3 x + 10}{4} \cdot 4

- 8 x - 12 = 3 x + 10

- 8 x - 3 x = 10 + 12

- 11 x = 22

x = \frac{22}{- 11}

$x = - 2$