Solve 0.75x+0.6left(x+1right)+0.4left(2x+1right)=0.53left(4x+2right)

$$0.75x+0.6 \left( x+1 \right) +0.4 \left( 2x+1 \right) = 0.53 \left( 4x+2 \right)$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 0.6 by x+1.

$$0.75x+0.6x+0.6+0.4\left(2x+1\right)=0.53\left(4x+2\right)$$

Combine 0.75x and 0.6x to get 1.35x.

$$1.35x+0.6+0.4\left(2x+1\right)=0.53\left(4x+2\right)$$

Use the distributive property to multiply 0.4 by 2x+1.

$$1.35x+0.6+0.8x+0.4=0.53\left(4x+2\right)$$

Combine 1.35x and 0.8x to get 2.15x.

$$2.15x+0.6+0.4=0.53\left(4x+2\right)$$

Add 0.6 and 0.4 to get 1.

$$2.15x+1=0.53\left(4x+2\right)$$

Use the distributive property to multiply 0.53 by 4x+2.

$$2.15x+1=2.12x+1.06$$

Subtract 2.12x from both sides.

$$2.15x+1-2.12x=1.06$$

Combine 2.15x and -2.12x to get 0.03x.

$$0.03x+1=1.06$$

Subtract 1 from both sides.

$$0.03x=1.06-1$$

Subtract 1 from 1.06 to get 0.06.

$$0.03x=0.06$$

Divide both sides by 0.03.

$$x=\frac{0.06}{0.03}$$

Expand \frac{0.06}{0.03} by multiplying both numerator and the denominator by 100.

$$x=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$x=2$$