To calculate: The solution of 6 by −4y≤7 by +10

Question

To calculate: The solution of 6 by −4y≤7 by +10

Nathaniel Kramer · Accepted Answer

Formula used:
The addition principle for inequalities:
For any real numbers a, b and c:
$a < b$ is equivalent to $a + c < b + c$
$a > b$ is equivalent to $a + c > b + c$
Similar statement holds for $\leq and \geq$
The multiplication principle for inequalities:
For any real numbers a and b, and for any negative number c,
$a < b$ is equivalent to $a c < b c$ .
$a > b$ is equivalent to $a c > b c$ .
Similar statement holds for $\leq and \geq$
The distributive property tells us how to solve expressions in the form of $a (b + c) = a b + a c$ .
The distributive property is sometimes called the distributive law of multiplication.
Calculation:
Consider, the equation $6 b y - 4 y \leq 7 b y + 10$ .
Subtract -7by on both the sides of the equation $6 b y - 4 y \leq 7 b y + 10$ .
$6 b y - 7 b y - 4 y \leq 7 b y - 7 b y + 10$
$- 1 b y - 4 y \leq 10$
$y (- b - 4) \leq 10$
Divide $(- b - 4)$ into both the sides of the equation $y (- b - 4) \leq 10$ .
$y \frac{(- b - 4)}{(- b - 4)} \leq \frac{10}{(- b - 4)}$
$y \geq \frac{10}{(- b - 4)} or - \frac{10}{b + 4}$
We reversed the inequality symbol when we divided $(- b - 4)$ to the inequality because $b > 0$ then $- b - 4 < 0$ .
Hence, the solution to inequality ${x ∣ x \geq - \frac{10}{(b + 4)}}$ .

To calculate: The solution of 6by-4y \leq 7by+10

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