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Solve for $k$ . $4 < \frac{k - 9}{-3}$

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Solve advanced linear inequalities

Full solution

Q. Solve for

k

.

4 < \frac{k - 9}{-3}

Multiply by $-3$ : First, we need to simplify the inequality by multiplying both sides by $-3$ to get rid of the fraction. Remember that multiplying by a negative number reverses the inequality sign. $\newline$ $4 < \frac{k - 9}{-3}$ $\newline$ $-3 \times 4 > -3 \times \left(k - \frac{9}{-3}\right)$
Perform multiplication: Now, perform the multiplication. $\newline$ $-12 > -3k + 9$
Isolate variable $k$ : Next, we isolate the variable $k$ on one side of the inequality by subtracting $9$ from both sides. $\newline$ $-12 - 9 > -3k + 9 - 9$
Simplify inequality: Simplify the inequality by combining like terms. $\newline$ $-21 > -3k$
Divide by $-3$ : Now, divide both sides by $-3$ to solve for $k$ . Remember to reverse the inequality sign because we are dividing by a negative number. $\newline$ $-21 / -3 < -3k / -3$
Perform division: Perform the division to find the value of $k$ . $7 < k$

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