Solve x600=1.2*(100*10^3-x)+2.4*(10*10^2-x)-2.4x

$$x 600 = 1.2 \times ( 100 \times 10 ^ { 3 } - x ) + 2.4 \times ( 10 \times 10 ^ { 2 } - x ) - 2.4 x$$

Solve for x

$$x=-\frac{x_{600}}{6}+20400$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x_{600}=1.2\left(100\times 10^{3}-x\right)+2.4\left(10^{3}-x\right)-2.4x$$

Calculate 10 to the power of 3 and get 1000.

$$x_{600}=1.2\left(100\times 1000-x\right)+2.4\left(10^{3}-x\right)-2.4x$$

Multiply 100 and 1000 to get 100000.

$$x_{600}=1.2\left(100000-x\right)+2.4\left(10^{3}-x\right)-2.4x$$

Use the distributive property to multiply 1.2 by 100000-x.

$$x_{600}=120000-1.2x+2.4\left(10^{3}-x\right)-2.4x$$

Calculate 10 to the power of 3 and get 1000.

$$x_{600}=120000-1.2x+2.4\left(1000-x\right)-2.4x$$

Use the distributive property to multiply 2.4 by 1000-x.

$$x_{600}=120000-1.2x+2400-2.4x-2.4x$$

Add 120000 and 2400 to get 122400.

$$x_{600}=122400-1.2x-2.4x-2.4x$$

Combine -1.2x and -2.4x to get -3.6x.

$$x_{600}=122400-3.6x-2.4x$$

Combine -3.6x and -2.4x to get -6x.

$$x_{600}=122400-6x$$

Swap sides so that all variable terms are on the left hand side.

$$122400-6x=x_{600}$$

Subtract 122400 from both sides.

$$-6x=x_{600}-122400$$

Divide both sides by -6.

$$\frac{-6x}{-6}=\frac{x_{600}-122400}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$x=\frac{x_{600}-122400}{-6}$$

Divide x_{600}-122400 by -6.

$$x=-\frac{x_{600}}{6}+20400$$

Solve for x_600

$$x_{600}=122400-6x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x_{600}=1.2\left(100\times 10^{3}-x\right)+2.4\left(10^{3}-x\right)-2.4x$$

Calculate 10 to the power of 3 and get 1000.

$$x_{600}=1.2\left(100\times 1000-x\right)+2.4\left(10^{3}-x\right)-2.4x$$

Multiply 100 and 1000 to get 100000.

$$x_{600}=1.2\left(100000-x\right)+2.4\left(10^{3}-x\right)-2.4x$$

Use the distributive property to multiply 1.2 by 100000-x.

$$x_{600}=120000-1.2x+2.4\left(10^{3}-x\right)-2.4x$$

Calculate 10 to the power of 3 and get 1000.

$$x_{600}=120000-1.2x+2.4\left(1000-x\right)-2.4x$$

Use the distributive property to multiply 2.4 by 1000-x.

$$x_{600}=120000-1.2x+2400-2.4x-2.4x$$

Add 120000 and 2400 to get 122400.

$$x_{600}=122400-1.2x-2.4x-2.4x$$

Combine -1.2x and -2.4x to get -3.6x.

$$x_{600}=122400-3.6x-2.4x$$

Combine -3.6x and -2.4x to get -6x.

$$x_{600}=122400-6x$$