Solve 10(x+2)+y+4=2[5(x-2)+4(y-1)]

$$10 ( x + 2 ) + y + 4 = 2 [ 5 ( x - 2 ) + 4 ( y - 1 ) ]$$

Solve for y

$$y = \frac{52}{7} = 7\frac{3}{7} = 7.428571428571429$$

Steps for Solving Linear Equation

Use the distributive property to multiply 10 by x+2.

$$10x+20+y+4=2\left(5\left(x-2\right)+4\left(y-1\right)\right)$$

Add 20 and 4 to get 24.

$$10x+24+y=2\left(5\left(x-2\right)+4\left(y-1\right)\right)$$

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

$$10x+24+y=2\left(5x-10+4\left(y-1\right)\right)$$

Use the distributive property to multiply 4 by y-1.

$$10x+24+y=2\left(5x-10+4y-4\right)$$

Subtract 4 from -10 to get -14.

$$10x+24+y=2\left(5x-14+4y\right)$$

Use the distributive property to multiply 2 by 5x-14+4y.

$$10x+24+y=10x-28+8y$$

Subtract 8y from both sides.

$$10x+24+y-8y=10x-28$$

Combine y and -8y to get -7y.

$$10x+24-7y=10x-28$$

Subtract 10x from both sides.

$$24-7y=10x-28-10x$$

Combine 10x and -10x to get 0.

$$24-7y=-28$$

Subtract 24 from both sides.

$$-7y=-28-24$$

Subtract 24 from -28 to get -52.

$$-7y=-52$$

Divide both sides by -7.

$$y=\frac{-52}{-7}$$

Fraction \frac{-52}{-7} can be simplified to \frac{52}{7} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{52}{7}$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

$$y = \frac{52}{7} = 7\frac{3}{7} = 7.428571428571429$$

Solve for x

$$x\in \mathrm{R}$$

$$y = \frac{52}{7} = 7\frac{3}{7} = 7.428571428571429$$