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

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

Solve for x

$x\geq \frac{9}{17}$

Solution Steps

Multiply both sides of the equation by $12$, the least common multiple of $4,3,2$. Since $12$ is positive, the inequality direction remains the same.

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

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

$$3x+9-4x\geq 12-6\left(3x-1\right)$$

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

$$-x+9\geq 12-6\left(3x-1\right)$$

Use the distributive property to multiply $-6$ by $3x-1$.

$$-x+9\geq 12-18x+6$$

Add $12$ and $6$ to get $18$.

$$-x+9\geq 18-18x$$

Add $18x$ to both sides.

$$-x+9+18x\geq 18$$

Combine $-x$ and $18x$ to get $17x$.

$$17x+9\geq 18$$

Subtract $9$ from both sides.

$$17x\geq 18-9$$

Subtract $9$ from $18$ to get $9$.

$$17x\geq 9$$

Divide both sides by $17$. Since $17$ is positive, the inequality direction remains the same.

$$x\geq \frac{9}{17}$$