Question

Solve each of the following equations and also check your results in each case:

1. (2x+5)/3 = 3x – 10

2. (a-8)/3 = (a-3)/2

3. (7y + 2)/5 = (6y – 5)/11

4. x – 2x + 2 – 16/3x + 5 = 3 – 7/2x

5. 1/2x + 7x – 6 = 7x + 1/4​

Answer 1

Answer:

Question 1:

$\implies \dfrac{2x+5}{3} = 3x - 10\\\\\\\implies 2x + 5 = 3 ( 3x - 10 )\\\\\\\implies 2x + 5 = 9x - 30\\\\\\\implies 9x - 2x = 30 + 5\\\\\\\implies 7x = 35\\\\\\\implies \boxed{ \bf{x = \dfrac{35}{7} = 5}}$

Question 2:

$\implies \dfrac{a-8}{3} = \dfrac{a-3}{2}\\\\\\\implies 2 ( a - 8 ) = 3 ( a - 3 )\\\\\implies 2a - 16 = 3a - 9\\\\\implies 3a - 2a = 9 - 16\\\\\implies \boxed{\bf{a=-7}}$

Question 3:

$\implies \dfrac{7y + 2 }{5} = \dfrac{6y - 5}{11}\\\\\\\implies 11 ( 7y + 2 ) = 5 ( 6y - 5 )\\\\\implies 77y + 22 = 30y - 25\\\\\implies 77y - 30y = -25 -22\\\\\implies 47y = -47\\\\\implies \boxed{ \bf{ y = \dfrac{-47}{47} = -1}}$

Question 4:

$\implies x - 2x + 2 - \dfrac{16x}{3} + 5 = 3 - \dfrac{7x}{2}\\\\\\\implies 2 - x - \dfrac{16x}{3} + 5 = 3 - \dfrac{7x}{2}\\\\\\\implies 7 + \dfrac{ -3x + 16x}{3} = \dfrac{6-7x}{2}\\\\\\\implies 7 + \dfrac{13x}{3} = \dfrac{6-7x}{2}\\\\\\\implies \dfrac{21 +13x}{3} = \dfrac{6-7x}{2}\\\\\\\implies 2 ( 21 + 13x ) = 3 ( 6 - 7x )\\\\\\\implies 42 + 26x = 18 - 21x\\\\\\\implies 26x + 21x = 18 - 42\\\\\\\implies 47x = -24\\\\\\\implies \boxed{ \bf{x = \dfrac{-24}{47}}}$

Question 5:

$\implies \dfrac{x}{2} + 7x - 6 = 7x + \dfrac{1}{4}\\\\\\\implies \dfrac{ x + 14x}{2} - 6 = \dfrac{28x + 1}{4}\\\\\\\implies \dfrac{15x}{2} - 6 = \dfrac{28x + 1}{4}\\\\\\\implies \dfrac{15x - 12}{2} = \dfrac{28x + 1}{4}\\\\\\\implies 4 ( 15x -12) = 2 ( 28x + 1)\\\\\\\implies 60x -48 = 56x + 2\\\\\\\implies 60x - 56x = 48 + 2\\\\\\\implies 4x = 50\\\\\\\implies \boxed{\bf{x = \dfrac{50}{4}}}$

Answer 2

$\huge\pink{\mid{\fbox{\underline{\underline{Answer}}}}\mid}$

Answer 1:-

$\frac{(2x+5)}{3} = 3x–10 \\\\ => 2x+ 5 = 3(3x–10) \\\\ => 2x+ 5 = 9x–30 \\\\ => 9x - 2x = 5+30 \\\\ => 7x = 35 \\ => x = \frac{35}{7} \\\\\large\bf \fbox{ x = 5}$

Answer 2:-

$\frac{(a-8)}{3} = \frac{(a-3)}{2} \\\\ => 2(a-8) = 3(a-3) \\\\ => 2a–16 = 3a–9 \\\\ => 3a - 2a = –16+9 \\\\ \large\bf\boxed {a = –7}$

Answer 3:-

$\frac{(7y+2)}{5} = \frac{(6y–5)}{11} \\\\ =>11(7y+2) = 5(6y-5) \\\\ => 77y+22 = 30y–25 \\\\ => 77y - 30y = –25–22 \\\\ => 47y = –47 \\\\ => y = \frac{-47}{47} \\\\ \large\bf\fbox{ y = –1}$

Answer 4:-

$x – 2x + 2 – \frac{16x}{3} + 5 = 3 – \frac{7x}{2} \\\\ => 7 – x – \frac{16x}{3} = 3 – \frac{7x}{2} \\\\ => 7 – x – 3 = \frac{16x}{3} – \frac{7x}{2} \\\\ => 4 – x = \frac{32x-21x}{6}\\\\ => 24 - 6x = 11x \\\\ => 6x+11x = 24 \\\\ => 17x = 24 \\\\ \large\bf\fbox{x = 24/17 }$

Answer 5:-

$\frac{1}{2x} + 7x – 6 = 7x + \frac{1}{4} \\\\ => \frac{1}{2x} = \frac{1}{4} + 6 \\\\ => \frac{1}{2x} = \frac{1+24}{4} \\\\ => \frac{1}{2x} = \frac{25}{4} \\\\ => x = \frac{25×2}{4} \\\\ \large \bf\boxed{ x = 12.5}$

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