Solve (x)/(2)-(1)/(4)((x)/(1)-(1)/(3))=(1)/(6)-x+1+(1)/(12) | 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

$$\frac{ x }{ 2 } - \frac{ 1 }{ 4 } ( \frac{ x }{ 1 } - \frac{ 1 }{ 3 } )= \frac{ 1 }{ 6 } -x+1+ \frac{ 1 }{ 12 }$$

Solve for x

$x=\frac{14}{15}\approx 0.933333333$

Steps for Solving Linear Equation

Multiply both sides of the equation by $12$, the least common multiple of $2,4,3,6,12$.

$$6x-3\left(\frac{x}{1}-\frac{1}{3}\right)=2-12x+12+1$$

Anything divided by one gives itself.

$$6x-3\left(x-\frac{1}{3}\right)=2-12x+12+1$$

Use the distributive property to multiply $-3$ by $x-\frac{1}{3}$.

$$6x-3x-3\left(-\frac{1}{3}\right)=2-12x+12+1$$

Multiply $-3$ times $-\frac{1}{3}$.

$$6x-3x+1=2-12x+12+1$$

Combine $6x$ and $-3x$ to get $3x$.

$$3x+1=2-12x+12+1$$

Add $2$ and $12$ to get $14$.

$$3x+1=14-12x+1$$

Add $14$ and $1$ to get $15$.

$$3x+1=15-12x$$

Add $12x$ to both sides.

$$3x+1+12x=15$$

Combine $3x$ and $12x$ to get $15x$.

$$15x+1=15$$

Subtract $1$ from both sides.

$$15x=15-1$$

Subtract $1$ from $15$ to get $14$.

$$15x=14$$

Divide both sides by $15$.

$$x=\frac{14}{15}$$