Solve a1/3x+71/2x=90

$$a \frac { 1 } { 3 } x + 7 \frac { 1 } { 2 } x = 90$$

Solve for a

$$a=-\frac{45}{2}+\frac{270}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$6a\times \frac{1}{3}x+3\left(7\times 2+1\right)x=540$$

Multiply 6 and \frac{1}{3} to get 2.

$$2ax+3\left(7\times 2+1\right)x=540$$

Multiply 7 and 2 to get 14.

$$2ax+3\left(14+1\right)x=540$$

Add 14 and 1 to get 15.

$$2ax+3\times 15x=540$$

Multiply 3 and 15 to get 45.

$$2ax+45x=540$$

Subtract 45x from both sides.

$$2ax=540-45x$$

The equation is in standard form.

$$2xa=540-45x$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{540-45x}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{540-45x}{2x}$$

Divide 540-45x by 2x.

$$a=-\frac{45}{2}+\frac{270}{x}$$

Solve for x

$$x=\frac{540}{2a+45}$$

$$a\neq -\frac{45}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$6a\times \frac{1}{3}x+3\left(7\times 2+1\right)x=540$$

Multiply 6 and \frac{1}{3} to get 2.

$$2ax+3\left(7\times 2+1\right)x=540$$

Multiply 7 and 2 to get 14.

$$2ax+3\left(14+1\right)x=540$$

Add 14 and 1 to get 15.

$$2ax+3\times 15x=540$$

Multiply 3 and 15 to get 45.

$$2ax+45x=540$$

Combine all terms containing x.

$$\left(2a+45\right)x=540$$

Divide both sides by 2a+45.

$$\frac{\left(2a+45\right)x}{2a+45}=\frac{540}{2a+45}$$

Dividing by 2a+45 undoes the multiplication by 2a+45.

$$x=\frac{540}{2a+45}$$