Question

# Solve the following inequations 5x−23−7x−35>x4

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Solution

## 5x−23−7x−35>x4⇒5(5x−2)−3(7x−3)15>x4⇒25x−10−21x+915>x44x−115>x4⇒4(4x−1)>15x[Multiplying both sides by 60 i.e. Lcm of 15 and 4]16x−4>15x ⇒16x−15x>4[Transposing 15 x to LHS and -4 to RHS]x > 4 ⇒x∈(4,∞)Hence the solution set of the given inequation is (4,∞) This can be graphed on the real number line as shown in figure

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