Solve 7(2x-1)-3(4x-1)=5(3x-2)-1

$$7 ( 2 x - 1 ) - 3 ( 4 x - 1 ) = 5 ( 3 x - 2 ) - 1$$

Solve for x

$$x=\frac{7}{13}\approx 0.538461538$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by 2x-1.

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

Use the distributive property to multiply -3 by 4x-1.

$$14x-7-12x+3=5\left(3x-2\right)-1$$

Combine 14x and -12x to get 2x.

$$2x-7+3=5\left(3x-2\right)-1$$

Add -7 and 3 to get -4.

$$2x-4=5\left(3x-2\right)-1$$

Use the distributive property to multiply 5 by 3x-2.

$$2x-4=15x-10-1$$

Subtract 1 from -10 to get -11.

$$2x-4=15x-11$$

Subtract 15x from both sides.

$$2x-4-15x=-11$$

Combine 2x and -15x to get -13x.

$$-13x-4=-11$$

Add 4 to both sides.

$$-13x=-11+4$$

Add -11 and 4 to get -7.

$$-13x=-7$$

Divide both sides by -13.

$$x=\frac{-7}{-13}$$

Fraction \frac{-7}{-13} can be simplified to \frac{7}{13} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{13}$$