Question

3x-5/2+x+2x-3/3=5/6-3x/2

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Answer 1

Given:

$3x - \frac{5}{2} + x + 2x - \frac{3}{3} = \frac{5}{6} - \frac{3x}{2}$

STEP BY STEP EXPLANATION:

$6x - \frac{5}{2} + x + 2x - 1 = \frac{5}{6} - \frac{ 3x}{2}$

Collect like terms

$6x - \frac{7}{2} = \frac{5}{6} - \frac{3x}{2}$

move the variable to left hand side and change its sign

$6x + \frac{3x}{2} = \frac{5}{6} + \frac{7}{2}$

Calculate the sum

$\frac{15}{2} x = \frac{5}{6} + \frac{7}{2}$

Multiply both side of equation by $\frac{2}{15}$

$x = \frac{26}{45}$

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$\boxed{\text{45x = 26}}$

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Hence verified !

Answer 2

Step-by-step explanation:

Given,

3x - 5² + x + 2x - 3³ = 56 - 3x²

=> 3x - 25 + 3x - 27 = 56 - 3x²

=> 6x - 52 = 56 - 3x²

=> 6x + 3x² = 56 + 52

=>3x² + 6x = 108

=> 3x² + 6x - 108 = 0

=> 3( x² + 2x - 36 ) = 0

=> x² + 2x - 36 = 0

Here it's an quadratic equation so we can solve it by 2 methods. Those are 1. QUADRATIC FORMULA and 2. SPLITTING MIDDLE TERM METHOD.

● For this equation we must use 1st method (i.e) QUADRATIC FORMULA METHOD.

QUADRATIC FORMULA : x = -b ± √b²-4ac/2a

here,

a = 1, b = 2, c = -36.

=> -2 ±√ 2² - 4(1)(-36) / 2(1)

=> -2 ± √ 4 + 144 / 2

=> -2 ± √ 148 / 2

=> -2 ± 2 √37 / 2

=> -2 + 2 √37 / 2 & -2 - 2 √37 / 2

=> 2( -1 + √37 ) / 2 & -2( 1 + √37

=> -1 + √37 & - ( 1 + √37 )

=> -1 + √37 & -1 - √37

■ THE ROOTS ARE -1 ± √37

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