Solve =4Deltax+(Deltax)^2-7Deltax/Deltax=Deltax-3

$$= \frac { 4 \Delta x + ( \Delta x ) ^ { 2 } - 7 \Delta x } { \Delta x } = \Delta x - 3$$

Solve for x

$$x\neq 0$$

$$\Delta \neq 0$$

Solution Steps

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x\Delta .

$$4\Delta x+\left(\Delta x\right)^{2}-7\Delta x=\Delta xx\Delta +x\Delta \left(-3\right)$$

Expand \left(\Delta x\right)^{2}.

$$4\Delta x+\Delta ^{2}x^{2}-7\Delta x=\Delta xx\Delta +x\Delta \left(-3\right)$$

Combine 4\Delta x and -7\Delta x to get -3\Delta x.

$$-3\Delta x+\Delta ^{2}x^{2}=\Delta xx\Delta +x\Delta \left(-3\right)$$

Multiply \Delta and \Delta to get \Delta ^{2}.

$$-3\Delta x+\Delta ^{2}x^{2}=\Delta ^{2}xx+x\Delta \left(-3\right)$$

Multiply x and x to get x^{2}.

$$-3\Delta x+\Delta ^{2}x^{2}=\Delta ^{2}x^{2}+x\Delta \left(-3\right)$$

Subtract \Delta ^{2}x^{2} from both sides.

$$-3\Delta x+\Delta ^{2}x^{2}-\Delta ^{2}x^{2}=x\Delta \left(-3\right)$$

Combine \Delta ^{2}x^{2} and -\Delta ^{2}x^{2} to get 0.

$$-3\Delta x=x\Delta \left(-3\right)$$

Subtract x\Delta \left(-3\right) from both sides.

$$-3\Delta x-x\Delta \left(-3\right)=0$$

Combine -3\Delta x and -x\Delta \left(-3\right) to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

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

Variable x cannot be equal to 0.

$$x\in \mathrm{R}\setminus 0$$

Solve for Δ

$$\Delta \neq 0$$

$$x\neq 0$$

Solution Steps

Variable \Delta cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x\Delta .

$$4\Delta x+\left(\Delta x\right)^{2}-7\Delta x=\Delta xx\Delta +x\Delta \left(-3\right)$$

Expand \left(\Delta x\right)^{2}.

$$4\Delta x+\Delta ^{2}x^{2}-7\Delta x=\Delta xx\Delta +x\Delta \left(-3\right)$$

Combine 4\Delta x and -7\Delta x to get -3\Delta x.

$$-3\Delta x+\Delta ^{2}x^{2}=\Delta xx\Delta +x\Delta \left(-3\right)$$

Multiply \Delta and \Delta to get \Delta ^{2}.

$$-3\Delta x+\Delta ^{2}x^{2}=\Delta ^{2}xx+x\Delta \left(-3\right)$$

Multiply x and x to get x^{2}.

$$-3\Delta x+\Delta ^{2}x^{2}=\Delta ^{2}x^{2}+x\Delta \left(-3\right)$$

Subtract \Delta ^{2}x^{2} from both sides.

$$-3\Delta x+\Delta ^{2}x^{2}-\Delta ^{2}x^{2}=x\Delta \left(-3\right)$$

Combine \Delta ^{2}x^{2} and -\Delta ^{2}x^{2} to get 0.

$$-3\Delta x=x\Delta \left(-3\right)$$

Subtract x\Delta \left(-3\right) from both sides.

$$-3\Delta x-x\Delta \left(-3\right)=0$$

Combine -3\Delta x and -x\Delta \left(-3\right) to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any \Delta .

$$\Delta \in \mathrm{R}$$

Variable \Delta cannot be equal to 0.

$$\Delta \in \mathrm{R}\setminus 0$$