Solve ( x ) (3a)/7 - (a - 2)/5 = a/3 + a/7; (xi) = | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$( x ) \frac { 3 a } { 7 } - \frac { a - 2 } { 5 } = \frac { a } { 3 } + \frac { a } { 7 }$$

Solve for a

$a=-\frac{42}{45x-71}$
$x\neq \frac{71}{45}$

Steps for Solving Linear Equation

Multiply both sides of the equation by $105$, the least common multiple of $7,5,3$.

$$15x\times 3a-21\left(a-2\right)=35a+15a$$

Multiply $15$ and $3$ to get $45$.

$$45xa-21\left(a-2\right)=35a+15a$$

Use the distributive property to multiply $-21$ by $a-2$.

$$45xa-21a+42=35a+15a$$

Combine $35a$ and $15a$ to get $50a$.

$$45xa-21a+42=50a$$

Subtract $50a$ from both sides.

$$45xa-21a+42-50a=0$$

Combine $-21a$ and $-50a$ to get $-71a$.

$$45xa-71a+42=0$$

Subtract $42$ from both sides. Anything subtracted from zero gives its negation.

$$45xa-71a=-42$$

Combine all terms containing $a$.

$$\left(45x-71\right)a=-42$$

Divide both sides by $45x-71$.

$$\frac{\left(45x-71\right)a}{45x-71}=-\frac{42}{45x-71}$$

Dividing by $45x-71$ undoes the multiplication by $45x-71$.

$$a=-\frac{42}{45x-71}$$

Solve for x

$x=\frac{71}{45}-\frac{14}{15a}$
$a\neq 0$

Steps for Solving Linear Equation

Multiply both sides of the equation by $105$, the least common multiple of $7,5,3$.

$$15x\times 3a-21\left(a-2\right)=35a+15a$$

Multiply $15$ and $3$ to get $45$.

$$45xa-21\left(a-2\right)=35a+15a$$

Use the distributive property to multiply $-21$ by $a-2$.

$$45xa-21a+42=35a+15a$$

Combine $35a$ and $15a$ to get $50a$.

$$45xa-21a+42=50a$$

Add $21a$ to both sides.

$$45xa+42=50a+21a$$

Combine $50a$ and $21a$ to get $71a$.

$$45xa+42=71a$$

Subtract $42$ from both sides.

$$45xa=71a-42$$

The equation is in standard form.

$$45ax=71a-42$$

Divide both sides by $45a$.

$$\frac{45ax}{45a}=\frac{71a-42}{45a}$$

Dividing by $45a$ undoes the multiplication by $45a$.

$$x=\frac{71a-42}{45a}$$

Divide $71a-42$ by $45a$.

$$x=\frac{71}{45}-\frac{14}{15a}$$