Solve 5(a+b)-2a+ab=4a+9b-(a+b)

$$5 ( a + b ) - 2 a + a b = 4 a + 9 b - ( a + b )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=3\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$5a+5b-2a+ab=4a+9b-\left(a+b\right)$$

Combine 5a and -2a to get 3a.

$$3a+5b+ab=4a+9b-\left(a+b\right)$$

To find the opposite of a+b, find the opposite of each term.

$$3a+5b+ab=4a+9b-a-b$$

Combine 4a and -a to get 3a.

$$3a+5b+ab=3a+9b-b$$

Combine 9b and -b to get 8b.

$$3a+5b+ab=3a+8b$$

Subtract 3a from both sides.

$$3a+5b+ab-3a=8b$$

Combine 3a and -3a to get 0.

$$5b+ab=8b$$

Subtract 5b from both sides.

$$ab=8b-5b$$

Combine 8b and -5b to get 3b.

$$ab=3b$$

The equation is in standard form.

$$ba=3b$$

Divide both sides by b.

$$\frac{ba}{b}=\frac{3b}{b}$$

Dividing by b undoes the multiplication by b.

$$a=\frac{3b}{b}$$

Divide 3b by b.

$$a=3$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=0\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&a=3\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$5a+5b-2a+ab=4a+9b-\left(a+b\right)$$

Combine 5a and -2a to get 3a.

$$3a+5b+ab=4a+9b-\left(a+b\right)$$

To find the opposite of a+b, find the opposite of each term.

$$3a+5b+ab=4a+9b-a-b$$

Combine 4a and -a to get 3a.

$$3a+5b+ab=3a+9b-b$$

Combine 9b and -b to get 8b.

$$3a+5b+ab=3a+8b$$

Subtract 8b from both sides.

$$3a+5b+ab-8b=3a$$

Combine 5b and -8b to get -3b.

$$3a-3b+ab=3a$$

Subtract 3a from both sides.

$$-3b+ab=3a-3a$$

Combine 3a and -3a to get 0.

$$-3b+ab=0$$

Combine all terms containing b.

$$\left(-3+a\right)b=0$$

The equation is in standard form.

$$\left(a-3\right)b=0$$

Divide 0 by -3+a.

$$b=0$$

Solve for a

$$\left\{\begin{matrix}\\a=3\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$5a+5b-2a+ab=4a+9b-\left(a+b\right)$$

Combine 5a and -2a to get 3a.

$$3a+5b+ab=4a+9b-\left(a+b\right)$$

To find the opposite of a+b, find the opposite of each term.

$$3a+5b+ab=4a+9b-a-b$$

Combine 4a and -a to get 3a.

$$3a+5b+ab=3a+9b-b$$

Combine 9b and -b to get 8b.

$$3a+5b+ab=3a+8b$$

Subtract 3a from both sides.

$$3a+5b+ab-3a=8b$$

Combine 3a and -3a to get 0.

$$5b+ab=8b$$

Subtract 5b from both sides.

$$ab=8b-5b$$

Combine 8b and -5b to get 3b.

$$ab=3b$$

The equation is in standard form.

$$ba=3b$$

Divide both sides by b.

$$\frac{ba}{b}=\frac{3b}{b}$$

Dividing by b undoes the multiplication by b.

$$a=\frac{3b}{b}$$

Divide 3b by b.

$$a=3$$

Solve for b

$$\left\{\begin{matrix}\\b=0\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=3\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$5a+5b-2a+ab=4a+9b-\left(a+b\right)$$

Combine 5a and -2a to get 3a.

$$3a+5b+ab=4a+9b-\left(a+b\right)$$

To find the opposite of a+b, find the opposite of each term.

$$3a+5b+ab=4a+9b-a-b$$

Combine 4a and -a to get 3a.

$$3a+5b+ab=3a+9b-b$$

Combine 9b and -b to get 8b.

$$3a+5b+ab=3a+8b$$

Subtract 8b from both sides.

$$3a+5b+ab-8b=3a$$

Combine 5b and -8b to get -3b.

$$3a-3b+ab=3a$$

Subtract 3a from both sides.

$$-3b+ab=3a-3a$$

Combine 3a and -3a to get 0.

$$-3b+ab=0$$

Combine all terms containing b.

$$\left(-3+a\right)b=0$$

The equation is in standard form.

$$\left(a-3\right)b=0$$

Divide 0 by -3+a.

$$b=0$$