# Inequalities – one variable Inequality – Exercise 5688

Exercise

Solve the inequality:

$$\frac{x+1}{2}<\frac{x+4}{5}-\frac{x+7}{10}$$

$$x< -1$$

Solution

$$\frac{x+1}{2}<\frac{x+4}{5}-\frac{x+7}{10}$$

In order to get rid of the fractions,multiply the inequality by 10:

$$5(x+1)<2(x+4)-(x+7)$$

$$5x+5<2x+8-x-7$$

$$5x-2x+x<8-7-5$$

$$4x<-4$$

$$x<-1$$

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