Solve (x-5)/(4)=(3x+4)/(2)-(7x-5)/(4) | 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

$$\frac{ x-5 }{ 4 } = \frac{ 3x+4 }{ 2 } - \frac{ 7x-5 }{ 4 }$$

Solve for x

$x=9$

Steps for Solving Linear Equation

Multiply both sides of the equation by $4$, the least common multiple of $4,2$.

$$x-5=2\left(3x+4\right)-\left(7x-5\right)$$

Use the distributive property to multiply $2$ by $3x+4$.

$$x-5=6x+8-\left(7x-5\right)$$

To find the opposite of $7x-5$, find the opposite of each term.

$$x-5=6x+8-7x-\left(-5\right)$$

The opposite of $-5$ is $5$.

$$x-5=6x+8-7x+5$$

Combine $6x$ and $-7x$ to get $-x$.

$$x-5=-x+8+5$$

Add $8$ and $5$ to get $13$.

$$x-5=-x+13$$

Add $x$ to both sides.

$$x-5+x=13$$

Combine $x$ and $x$ to get $2x$.

$$2x-5=13$$

Add $5$ to both sides.

$$2x=13+5$$

Add $13$ and $5$ to get $18$.

$$2x=18$$

Divide both sides by $2$.

$$x=\frac{18}{2}$$

Divide $18$ by $2$ to get $9$.

$$x=9$$