Solve-3x-5-4x-3-where-x-R-

Question Number 109004 by Don08q last updated on 20/Aug/20

\overset{}{} S o l v e ∣ 3 x + 5 ∣ = ∣ 4 x - 3 ∣

w h e r e x \in R

Answered by bemath last updated on 20/Aug/20

\Rightarrow (3 x + 5 + 4 x - 3) (3 x + 5 - 4 x + 3) = 0

(7 x + 2) (8 - x) = 0 \to {\begin{cases} x = 8 \\ x = - \frac{2}{7} \end{cases}

c h e k i n g \to {\begin{cases} ∣ 24 + 5 ∣=∣ 32 - 3 ∣ ⟨ t r u e ⟩ \\ ∣ \frac{- 6 + 35}{7} ∣ = ∣ \frac{- 8 - 21}{7} ∣ ⟨ t r u e ⟩ \end{cases}

Commented by john santu last updated on 20/Aug/20

s h o r t c u t

Answered by Aziztisffola last updated on 20/Aug/20

∣ 3 x + 5 ∣ = ∣ 4 x - 3 ∣\Rightarrow {\begin{cases} 3 x + 5 = 4 x - 3 \\ 3 x + 5 = - 4 x + 3 \end{cases}

{\begin{cases} x = 8 \\ x = - \frac{2}{7} \end{cases}

Commented by Rasheed.Sindhi last updated on 21/Aug/20

S t a n d a r d w a y!

Answered by floor(10²Eta[1]) last updated on 20/Aug/20

squaring both sides :

{9 x}^{2} + 30 x + 25 = {16 x}^{2} - 24 x + 9

{7 x}^{2} - 54 x - 16 = 0

x = \frac{54 \pm \sqrt{54^{2} + 4.7.16}}{2.7} = \frac{27 \pm 29}{7}

\Rightarrow x = \frac{- 2}{7}, x = 8

Answered by Rasheed.Sindhi last updated on 21/Aug/20

∣ 3 x + 5 ∣ = ∣ 4 x - 3 ∣\Rightarrow \frac{∣ 3 x + 5 ∣}{∣ 4 x - 3 ∣} = 1

\Rightarrow∣ \frac{3 x + 5}{4 x - 3} ∣= 1

\Rightarrow \frac{3 x + 5}{4 x - 3} = 1 \lor \frac{3 x + 5}{4 x - 3} = - 1

4 x - 3 = 3 x + 5 \lor 3 x + 5 = - 4 x + 3

x = 8 \lor x = - 2 / 7