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

$$\frac{ 3x-1 }{ 6 } \leq x+ \frac{ x-1 }{ 4 } - \frac{ x+2 }{ 3 }$$

Solve for x

$x\geq \frac{9}{5}$

Solution Steps

Multiply both sides of the equation by $12$, the least common multiple of $6,4,3$. Since $12$ is positive, the inequality direction remains the same.

$$2\left(3x-1\right)\leq 12x+3\left(x-1\right)-4\left(x+2\right)$$

Use the distributive property to multiply $2$ by $3x-1$.

$$6x-2\leq 12x+3\left(x-1\right)-4\left(x+2\right)$$

Use the distributive property to multiply $3$ by $x-1$.

$$6x-2\leq 12x+3x-3-4\left(x+2\right)$$

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

$$6x-2\leq 15x-3-4\left(x+2\right)$$

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

$$6x-2\leq 15x-3-4x-8$$

Combine $15x$ and $-4x$ to get $11x$.

$$6x-2\leq 11x-3-8$$

Subtract $8$ from $-3$ to get $-11$.

$$6x-2\leq 11x-11$$

Subtract $11x$ from both sides.

$$6x-2-11x\leq -11$$

Combine $6x$ and $-11x$ to get $-5x$.

$$-5x-2\leq -11$$

Add $2$ to both sides.

$$-5x\leq -11+2$$

Add $-11$ and $2$ to get $-9$.

$$-5x\leq -9$$

Divide both sides by $-5$. Since $-5$ is negative, the inequality direction is changed.

$$x\geq \frac{-9}{-5}$$

Fraction $\frac{-9}{-5}$ can be simplified to $\frac{9}{5}$ by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{9}{5}$$