Answer:
x = [tex]\frac{1}{10}[/tex]
Explanation:
In an equation our aim is to find the value of the whatever we are finding but in this case it is 'x' as well as keeping the equation balanced. If we did one operation on only one side then the equation has changed so it's important to remember that is you do an operation one side you must do it on the other otherwise the whole equation will change
[tex]\frac{6x-3}{2x+7} = \frac{3x-2}{x+5}[/tex]
→ First step is to cross multiply the denominators to get rid of the denominators so ( 6x - 3 ) × ( x + 5 ) and ( 3x - 2 ) × ( 2x + 7 )
( 6x - 3 ) ( x + 5 ) = ( 3x - 2 ) ( 2x + 7 )
→ Expand out the brackets using FOIL, first two, outer two, inner two and last two
6x² + 30x - 3x - 15 = 6x² + 21x - 4x - 14
→ Simplify and collect the 'x' terms together
6x² + 27x - 15 = 6x² + 17x - 14
→ Minus 6x² from both sides to isolate the whole numbers as well as the 'x' values
27x - 15 = 17x - 14
→ Minus 17x from both sides to collect the 'x' terms
10x - 15 = -14
→ Add - 15 to both sides to isolate 10
10x = 1
→ Divide both sides by 10 to isolate x
x = [tex]\frac{1}{10}[/tex]
