Solve 6-2(2x-1/2)=4x-2(3/4-3x)

$$6 - 2 ( 2 x - \frac { 1 } { 2 } ) = 4 x - 2 ( \frac { 3 } { 4 } - 3 x )$$

Solve for x

$$x=\frac{17}{28}\approx 0.607142857$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by 2x-\frac{1}{2}.

$$6-4x-2\left(-\frac{1}{2}\right)=4x-2\left(\frac{3}{4}-3x\right)$$

Multiply -2 times -\frac{1}{2}.

$$6-4x+1=4x-2\left(\frac{3}{4}-3x\right)$$

Add 6 and 1 to get 7.

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

Use the distributive property to multiply -2 by \frac{3}{4}-3x.

$$7-4x=4x-2\times \frac{3}{4}+6x$$

Express -2\times \frac{3}{4} as a single fraction.

$$7-4x=4x+\frac{-2\times 3}{4}+6x$$

Multiply -2 and 3 to get -6.

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

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$7-4x=4x-\frac{3}{2}+6x$$

Combine 4x and 6x to get 10x.

$$7-4x=10x-\frac{3}{2}$$

Subtract 10x from both sides.

$$7-4x-10x=-\frac{3}{2}$$

Combine -4x and -10x to get -14x.

$$7-14x=-\frac{3}{2}$$

Subtract 7 from both sides.

$$-14x=-\frac{3}{2}-7$$

Convert 7 to fraction \frac{14}{2}.

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

Since -\frac{3}{2} and \frac{14}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 14 from -3 to get -17.

$$-14x=-\frac{17}{2}$$

Divide both sides by -14.

$$x=\frac{-\frac{17}{2}}{-14}$$

Express \frac{-\frac{17}{2}}{-14} as a single fraction.

$$x=\frac{-17}{2\left(-14\right)}$$

Multiply 2 and -14 to get -28.

$$x=\frac{-17}{-28}$$

Fraction \frac{-17}{-28} can be simplified to \frac{17}{28} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{17}{28}$$