Solve 2+(x)/(4) <= (2x)/(5) | 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

$$2+ \frac{ x }{ 4 } \leq \frac{ 2x }{ 5 }$$

Solve for x

$x\geq \frac{40}{3}$

Solution Steps

Multiply both sides of the equation by $20$, the least common multiple of $4,5$. Since $20$ is positive, the inequality direction remains the same.

$$40+5x\leq 4\times 2x$$

Multiply $4$ and $2$ to get $8$.

$$40+5x\leq 8x$$

Subtract $8x$ from both sides.

$$40+5x-8x\leq 0$$

Combine $5x$ and $-8x$ to get $-3x$.

$$40-3x\leq 0$$

Subtract $40$ from both sides. Anything subtracted from zero gives its negation.

$$-3x\leq -40$$

Divide both sides by $-3$. Since $-3$ is negative, the inequality direction is changed.

$$x\geq \frac{-40}{-3}$$

Fraction $\frac{-40}{-3}$ can be simplified to $\frac{40}{3}$ by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{40}{3}$$