Solve the following system of equations in R.

$5 x - 7 < 3 (x + 3), 1 - \frac{3 x}{2} \geq x - 4$

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Solution

Consider the first inequation,

$5 x - 7 < 3 (x + 3) 5 x - 7 < 3 x + 9 5 x - 3 x < 9 + 7 2 x < 16 x < 8 . . . (i)$

Consider the second inequation,

$1 - \frac{3 x}{2} \geq x - 4 \frac{- 3 x}{2} - x \geq - 4 - 1 \frac{- 3 x - 2 x}{2} \geq - 5 - 5 x > - 10 x \leq 2 . . . (i i)$

From (i) and (ii), $(- \infty, 2)$ is the solution set of the simultaneous equations.

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