Solve (x 1)/4-(4x 1)/5≤(7-3x)/10

Evaluate

\frac{x \times 1}{4} - \frac{4 x \times 1}{5} \leq \frac{7 - 3 x}{10}

Simplify

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\frac{x}{4} - \frac{4 x}{5} \leq \frac{7 - 3 x}{10}

Multiply both sides of the inequality by 20

(\frac{x}{4} - \frac{4 x}{5}) \times 20 \leq \frac{7 - 3 x}{10} \times 20

Multiply the terms

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5 x - 16 x \leq \frac{7 - 3 x}{10} \times 20

Multiply the terms

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5 x - 16 x \leq 14 - 6 x

Simplify

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- 11 x \leq 14 - 6 x

Move the variable to the left side

- 11 x + 6 x \leq 14

Add the terms

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- 5 x \leq 14

Change the signs on both sides of the inequality and flip the inequality sign

5 x \geq - 14

Divide both sides

\frac{5 x}{5} \geq \frac{- 14}{5}

Divide the numbers

x \geq \frac{- 14}{5}

Solution

x \geq - \frac{14}{5}

Alternative Form

x \in [- \frac{14}{5}, + \infty)

Solve the inequality