Solve 3{2x-1-[3(2x-1)-3]}=5

$$3 \{ 2 x - 1 - [ 3 ( 2 x - 1 ) - 3 ] \} = 5$$

Solve for x

$$x=\frac{5}{6}\approx 0.833333333$$

Steps for Solving Linear Equation

Divide both sides by 3.

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

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

$$2x-1-\left(6x-3-3\right)=\frac{5}{3}$$

Subtract 3 from -3 to get -6.

$$2x-1-\left(6x-6\right)=\frac{5}{3}$$

To find the opposite of 6x-6, find the opposite of each term.

$$2x-1-6x-\left(-6\right)=\frac{5}{3}$$

The opposite of -6 is 6.

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

Combine 2x and -6x to get -4x.

$$-4x-1+6=\frac{5}{3}$$

Add -1 and 6 to get 5.

$$-4x+5=\frac{5}{3}$$

Subtract 5 from both sides.

$$-4x=\frac{5}{3}-5$$

Convert 5 to fraction \frac{15}{3}.

$$-4x=\frac{5}{3}-\frac{15}{3}$$

Since \frac{5}{3} and \frac{15}{3} have the same denominator, subtract them by subtracting their numerators.

$$-4x=\frac{5-15}{3}$$

Subtract 15 from 5 to get -10.

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

Divide both sides by -4.

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

Express \frac{-\frac{10}{3}}{-4} as a single fraction.

$$x=\frac{-10}{3\left(-4\right)}$$

Multiply 3 and -4 to get -12.

$$x=\frac{-10}{-12}$$

Reduce the fraction \frac{-10}{-12} to lowest terms by extracting and canceling out -2.

$$x=\frac{5}{6}$$