Solve 5x-2(2x-7)=2(3x-1)+7/2

$$5x-2(2x-7)=2(3x-1)+ \frac{ 7 }{ 2 }$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by 2x-7.

$$5x-4x+14=2\left(3x-1\right)+\frac{7}{2}$$

Combine 5x and -4x to get x.

$$x+14=2\left(3x-1\right)+\frac{7}{2}$$

Use the distributive property to multiply 2 by 3x-1.

$$x+14=6x-2+\frac{7}{2}$$

Convert -2 to fraction -\frac{4}{2}.

$$x+14=6x-\frac{4}{2}+\frac{7}{2}$$

Since -\frac{4}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$x+14=6x+\frac{-4+7}{2}$$

Add -4 and 7 to get 3.

$$x+14=6x+\frac{3}{2}$$

Subtract 6x from both sides.

$$x+14-6x=\frac{3}{2}$$

Combine x and -6x to get -5x.

$$-5x+14=\frac{3}{2}$$

Subtract 14 from both sides.

$$-5x=\frac{3}{2}-14$$

Convert 14 to fraction \frac{28}{2}.

$$-5x=\frac{3}{2}-\frac{28}{2}$$

Since \frac{3}{2} and \frac{28}{2} have the same denominator, subtract them by subtracting their numerators.

$$-5x=\frac{3-28}{2}$$

Subtract 28 from 3 to get -25.

$$-5x=-\frac{25}{2}$$

Divide both sides by -5.

$$x=\frac{-\frac{25}{2}}{-5}$$

Express \frac{-\frac{25}{2}}{-5} as a single fraction.

$$x=\frac{-25}{2\left(-5\right)}$$

Multiply 2 and -5 to get -10.

$$x=\frac{-25}{-10}$$

Reduce the fraction \frac{-25}{-10} to lowest terms by extracting and canceling out -5.

$$x=\frac{5}{2}$$