Haya, tuendelee na swali hili la hesabu:

Question

ScanSolve AI Tutor · Accepted Answer

Haya, tuendelee na swali hili la hesabu:

Solve for $x$

\frac{x+6}{4} + \frac{x-3}{5} = \frac{5x-4}{8}

Tafuta Kigawo Kidogo cha Pamoja (LCM) cha madhehebu (denominators) 4, 5, na 8.
LCM(4, 5, 8) = 40.
Zidisha kila neno katika mlinganyo kwa LCM ili kuondoa madhehebu.
$40 \left(\frac{x+6}{4}\right) + 40 \left(\frac{x-3}{5}\right) = 40 \left(\frac{5x-4}{8}\right)$
Rahisisha kila neno.
$10(x+6) + 8(x-3) = 5(5x-4)$
Fungua mabano kwa kuzidisha.
$10x + 60 + 8x - 24 = 25x - 20$
Unganisha maneno yanayofanana upande wa kushoto wa mlinganyo.
$(10x + 8x) + (60 - 24) = 25x - 20$ $18x + 36 = 25x - 20$
Peleka maneno yote yenye $x$ upande mmoja na namba zisizo na $x$ upande mwingine.
Toa $18x$ kutoka pande zote mbili:
$36 = 25x - 18x - 20$ $36 = 7x - 20$
Ongeza 20 kwa pande zote mbili:
$36 + 20 = 7x$ $56 = 7x$
Gawanya pande zote mbili kwa 7 ili kupata thamani ya $x$ .
$\frac{56}{7} = x$ $x = 8$
Thamani ya $x$ ni:
$8$

Answer