Solve 4*[9-5(x-2)]+3(3x-5)=2*[3(x-5)+17]-4

$$4 \cdot [ 9 - 5 ( x - 2 ) ] + 3 ( 3 x - 5 ) = 2 \cdot [ 3 ( x - 5 ) + 17 ] - 4$$

Solve for x

$$x = \frac{61}{17} = 3\frac{10}{17} \approx 3.588235294$$

Steps for Solving Linear Equation

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

$$4\left(9-5x+10\right)+3\left(3x-5\right)=2\left(3\left(x-5\right)+17\right)-4$$

Add 9 and 10 to get 19.

$$4\left(19-5x\right)+3\left(3x-5\right)=2\left(3\left(x-5\right)+17\right)-4$$

Use the distributive property to multiply 4 by 19-5x.

$$76-20x+3\left(3x-5\right)=2\left(3\left(x-5\right)+17\right)-4$$

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

$$76-20x+9x-15=2\left(3\left(x-5\right)+17\right)-4$$

Combine -20x and 9x to get -11x.

$$76-11x-15=2\left(3\left(x-5\right)+17\right)-4$$

Subtract 15 from 76 to get 61.

$$61-11x=2\left(3\left(x-5\right)+17\right)-4$$

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

$$61-11x=2\left(3x-15+17\right)-4$$

Add -15 and 17 to get 2.

$$61-11x=2\left(3x+2\right)-4$$

Use the distributive property to multiply 2 by 3x+2.

$$61-11x=6x+4-4$$

Subtract 4 from 4 to get 0.

$$61-11x=6x$$

Subtract 6x from both sides.

$$61-11x-6x=0$$

Combine -11x and -6x to get -17x.

$$61-17x=0$$

Subtract 61 from both sides. Anything subtracted from zero gives its negation.

$$-17x=-61$$

Divide both sides by -17.

$$x=\frac{-61}{-17}$$

Fraction \frac{-61}{-17} can be simplified to \frac{61}{17} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{61}{17}$$