Question

3/7(7x-1)-(2x-1-x/2)=x+3/2​

Answer 1

Question

Solve ⇒ $\frac{3}{7}(7x-1)-(2x-1-\frac{x}{2})=x+\frac{3}{2}$

$\rule{300}{1}$

Answer

Let's solve your equation step-by-step.

$\frac{3}{7}(7x-1)-(2x-1-\frac{x}{2})=x+\frac{3}{2}$

Step 1: Simplify both sides of the equation.

⇒ $\frac{3}{7}(7x-1)-(2x-1-\frac{x}{2})=x+\frac{3}{2}$

(Distribute the Negative Sign)

⇒ $\frac{3}{7}(7x-1)+-1(2x-1-\frac{x}{2})=x+\frac{3}{2}$

⇒ $\frac{3}{7}(7x-1)+-1(2x)+(-1)(-1)+-1(\frac{-1}{2} x)=x+\frac{3}{2}$

⇒ $\frac{3}{7} (7x-1)+-2x+1+\frac{1}{2}x =x+\frac{3}{2}$

(Distribute)

⇒ $(\frac{3}{7})(7x)+(\frac{3}{7})(-1)+-2x+1+\frac{1}{2}x=x+\frac{3}{2}$

⇒ $3x+\frac{-3}{7}+-2x+1+\frac{1}{2}x = x+ \frac{3}{2}$

(Combine Like Terms)

⇒ $(3x+-2x+\frac{1}{2}x )+(\frac{-3}{7} +1)=x+\frac{3}{2}$

⇒ $\frac{3}{2}x+\frac{4}{7}=x+\frac{3}{2}$

Step 2: Subtract x from both sides.

⇒ $\frac{3}{2}x+\frac{4}{7}-x=x+\frac{3}{2}-x$

⇒ $\frac{1}{2}x+\frac{4}{7}=\frac{3}{2}$

Step 3: Subtract $\frac{4}{7}$ from both sides.

⇒ $\frac{1}{2}x+\frac{4}{7}-\frac{4}{7} =\frac{3}{2}-\frac{4}{7}$

⇒ $\frac{1}{2}x=\frac{13}{14}$

Step 4: Multiply both sides by 2.

⇒ $2\times \frac{1}{2}x=2\times \frac{13}{14}$

⇒ $x=\frac{13}{7}$

$\bf \therefore x=\frac{13}{7} \ in \ the \ equation =>\ \frac{3}{7}(7x-1)-(2x-1-\frac{x}{2})=x+\frac{3}{2}$

$\rule{300}{1}$

Answer 2

$\sf \frac{3}{4} \bigg(7x - 1 \bigg) - \bigg(2x - \frac{1 - x}{2} \bigg) = x + \frac{3}{2} \\ \\ \\ \sf \frac{21x - 3}{4} - 2x + \frac{1 - x}{2} = x + \frac{3}{2} \\ \\ \\ \sf \: \frac{21x - 3 - 8x - 2 - 2x}{ \cancel{42}} = 2x + \frac{3}{ \cancel{2}} \\ \\ \\ \sf \: 21x - 3 - 8x + 2 - 2x = 4x + 6 \\ \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 11x - 4x = 1 + 6 \\ \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 7x = 7 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf x = 1 }$