Solve (a - 5)/4 + 1/5 = a - (2a - 7)/5 ( | 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

$$\frac { a - 5 } { 4 } + \frac { 1 } { 5 } = a - \frac { 2 a - 7 } { 5 }$$

Solve for a

$a=-7$

Steps for Solving Linear Equation

Multiply both sides of the equation by $20$, the least common multiple of $4,5$.

$$5\left(a-5\right)+4=20a-4\left(2a-7\right)$$

Use the distributive property to multiply $5$ by $a-5$.

$$5a-25+4=20a-4\left(2a-7\right)$$

Add $-25$ and $4$ to get $-21$.

$$5a-21=20a-4\left(2a-7\right)$$

Use the distributive property to multiply $-4$ by $2a-7$.

$$5a-21=20a-8a+28$$

Combine $20a$ and $-8a$ to get $12a$.

$$5a-21=12a+28$$

Subtract $12a$ from both sides.

$$5a-21-12a=28$$

Combine $5a$ and $-12a$ to get $-7a$.

$$-7a-21=28$$

Add $21$ to both sides.

$$-7a=28+21$$

Add $28$ and $21$ to get $49$.

$$-7a=49$$

Divide both sides by $-7$.

$$a=\frac{49}{-7}$$

Divide $49$ by $-7$ to get $-7$.

$$a=-7$$