Solve (x - 5)/3 - (x - 3)/4 = x/2 - 1 | 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

$$\frac{x-5}{3}-\frac{x-3}{4}=\frac{x}{2}-1$$

Solve for x

$x=\frac{1}{5}=0.2$

Steps for Solving Linear Equation

Multiply both sides of the equation by $12$, the least common multiple of $3,4,2$.

$$4\left(x-5\right)-3\left(x-3\right)=6x-12$$

Use the distributive property to multiply $4$ by $x-5$.

$$4x-20-3\left(x-3\right)=6x-12$$

Use the distributive property to multiply $-3$ by $x-3$.

$$4x-20-3x+9=6x-12$$

Combine $4x$ and $-3x$ to get $x$.

$$x-20+9=6x-12$$

Add $-20$ and $9$ to get $-11$.

$$x-11=6x-12$$

Subtract $6x$ from both sides.

$$x-11-6x=-12$$

Combine $x$ and $-6x$ to get $-5x$.

$$-5x-11=-12$$

Add $11$ to both sides.

$$-5x=-12+11$$

Add $-12$ and $11$ to get $-1$.

$$-5x=-1$$

Divide both sides by $-5$.

$$x=\frac{-1}{-5}$$

Fraction $\frac{-1}{-5}$ can be simplified to $\frac{1}{5}$ by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{5}$$