Solve (a+b)(-5)=a(-5)+b(-5)

$$( a + b ) ( - 5 ) = a ( - 5 ) + b ( - 5 )$$

Solve for a (complex solution)

$$a\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply a+b by -5.

$$-5a-5b=a\left(-5\right)+b\left(-5\right)$$

Subtract a\left(-5\right) from both sides.

$$-5a-5b-a\left(-5\right)=b\left(-5\right)$$

Combine -5a and -a\left(-5\right) to get 0.

$$-5b=b\left(-5\right)$$

Cancel out -5 on both sides.

$$b=b$$

Reorder the terms.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{C}$$

Solve for b (complex solution)

$$b\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply a+b by -5.

$$-5a-5b=a\left(-5\right)+b\left(-5\right)$$

Subtract b\left(-5\right) from both sides.

$$-5a-5b-b\left(-5\right)=a\left(-5\right)$$

Combine -5b and -b\left(-5\right) to get 0.

$$-5a=a\left(-5\right)$$

Cancel out -5 on both sides.

$$a=a$$

Reorder the terms.

$$\text{true}$$

This is true for any b.

$$b\in \mathrm{C}$$

Solve for a

$$a\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply a+b by -5.

$$-5a-5b=a\left(-5\right)+b\left(-5\right)$$

Subtract a\left(-5\right) from both sides.

$$-5a-5b-a\left(-5\right)=b\left(-5\right)$$

Combine -5a and -a\left(-5\right) to get 0.

$$-5b=b\left(-5\right)$$

Cancel out -5 on both sides.

$$b=b$$

Reorder the terms.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$

Solve for b

$$b\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply a+b by -5.

$$-5a-5b=a\left(-5\right)+b\left(-5\right)$$

Subtract b\left(-5\right) from both sides.

$$-5a-5b-b\left(-5\right)=a\left(-5\right)$$

Combine -5b and -b\left(-5\right) to get 0.

$$-5a=a\left(-5\right)$$

Cancel out -5 on both sides.

$$a=a$$

Reorder the terms.

$$\text{true}$$

This is true for any b.

$$b\in \mathrm{R}$$