Solve 9ax+2b/3+8ax+7b/5=b-8ax+5b/15

$$\frac { 9 a x + 2 b } { 3 } + \frac { 8 a x + 7 b } { 5 } = b - \frac { 8 a x + 5 b } { 15 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{3b}{11x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5,15.

$$5\left(9ax+2b\right)+3\left(8ax+7b\right)=15b-\left(8ax+5b\right)$$

Use the distributive property to multiply 5 by 9ax+2b.

$$45ax+10b+3\left(8ax+7b\right)=15b-\left(8ax+5b\right)$$

Use the distributive property to multiply 3 by 8ax+7b.

$$45ax+10b+24ax+21b=15b-\left(8ax+5b\right)$$

Combine 45ax and 24ax to get 69ax.

$$69ax+10b+21b=15b-\left(8ax+5b\right)$$

Combine 10b and 21b to get 31b.

$$69ax+31b=15b-\left(8ax+5b\right)$$

To find the opposite of 8ax+5b, find the opposite of each term.

$$69ax+31b=15b-8ax-5b$$

Combine 15b and -5b to get 10b.

$$69ax+31b=10b-8ax$$

Add 8ax to both sides.

$$69ax+31b+8ax=10b$$

Combine 69ax and 8ax to get 77ax.

$$77ax+31b=10b$$

Subtract 31b from both sides.

$$77ax=10b-31b$$

Combine 10b and -31b to get -21b.

$$77ax=-21b$$

The equation is in standard form.

$$77xa=-21b$$

Divide both sides by 77x.

$$\frac{77xa}{77x}=-\frac{21b}{77x}$$

Dividing by 77x undoes the multiplication by 77x.

$$a=-\frac{21b}{77x}$$

Divide -21b by 77x.

$$a=-\frac{3b}{11x}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{3b}{11x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5,15.

$$5\left(9ax+2b\right)+3\left(8ax+7b\right)=15b-\left(8ax+5b\right)$$

Use the distributive property to multiply 5 by 9ax+2b.

$$45ax+10b+3\left(8ax+7b\right)=15b-\left(8ax+5b\right)$$

Use the distributive property to multiply 3 by 8ax+7b.

$$45ax+10b+24ax+21b=15b-\left(8ax+5b\right)$$

Combine 45ax and 24ax to get 69ax.

$$69ax+10b+21b=15b-\left(8ax+5b\right)$$

Combine 10b and 21b to get 31b.

$$69ax+31b=15b-\left(8ax+5b\right)$$

To find the opposite of 8ax+5b, find the opposite of each term.

$$69ax+31b=15b-8ax-5b$$

Combine 15b and -5b to get 10b.

$$69ax+31b=10b-8ax$$

Add 8ax to both sides.

$$69ax+31b+8ax=10b$$

Combine 69ax and 8ax to get 77ax.

$$77ax+31b=10b$$

Subtract 31b from both sides.

$$77ax=10b-31b$$

Combine 10b and -31b to get -21b.

$$77ax=-21b$$

The equation is in standard form.

$$77xa=-21b$$

Divide both sides by 77x.

$$\frac{77xa}{77x}=-\frac{21b}{77x}$$

Dividing by 77x undoes the multiplication by 77x.

$$a=-\frac{21b}{77x}$$

Divide -21b by 77x.

$$a=-\frac{3b}{11x}$$

Solve for b

$$b=-\frac{11ax}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5,15.

$$5\left(9ax+2b\right)+3\left(8ax+7b\right)=15b-\left(8ax+5b\right)$$

Use the distributive property to multiply 5 by 9ax+2b.

$$45ax+10b+3\left(8ax+7b\right)=15b-\left(8ax+5b\right)$$

Use the distributive property to multiply 3 by 8ax+7b.

$$45ax+10b+24ax+21b=15b-\left(8ax+5b\right)$$

Combine 45ax and 24ax to get 69ax.

$$69ax+10b+21b=15b-\left(8ax+5b\right)$$

Combine 10b and 21b to get 31b.

$$69ax+31b=15b-\left(8ax+5b\right)$$

To find the opposite of 8ax+5b, find the opposite of each term.

$$69ax+31b=15b-8ax-5b$$

Combine 15b and -5b to get 10b.

$$69ax+31b=10b-8ax$$

Subtract 10b from both sides.

$$69ax+31b-10b=-8ax$$

Combine 31b and -10b to get 21b.

$$69ax+21b=-8ax$$

Subtract 69ax from both sides.

$$21b=-8ax-69ax$$

Combine -8ax and -69ax to get -77ax.

$$21b=-77ax$$

Divide both sides by 21.

$$\frac{21b}{21}=-\frac{77ax}{21}$$

Dividing by 21 undoes the multiplication by 21.

$$b=-\frac{77ax}{21}$$

Divide -77ax by 21.

$$b=-\frac{11ax}{3}$$