Question

1. \\(\frac{x}{-3} - 2 < -4\\)\
2. \\(-3 \geq 6x + 39\\)

Explanation:

Problem 3: Solve \(\boldsymbol{\frac{x}{-3}-2 < -4}\)

Step1: Add 2 to both sides

To isolate the term with \(x\), we add 2 to both sides of the inequality.
\(\frac{x}{-3}-2 + 2< -4 + 2\)
Simplifying, we get \(\frac{x}{-3}< -2\)

Step2: Multiply both sides by -3 (and reverse inequality)

When multiplying or dividing an inequality by a negative number, the direction of the inequality sign reverses. We multiply both sides by -3.
\(\frac{x}{-3}\times(-3)> -2\times(-3)\)
Simplifying, we get \(x > 6\)

Step1: Subtract 39 from both sides

To isolate the term with \(x\), we subtract 39 from both sides of the inequality.
\(-3-39\geq6x + 39-39\)
Simplifying, we get \(-42\geq6x\)

Step2: Divide both sides by 6

We divide both sides by 6 to solve for \(x\).
\(\frac{-42}{6}\geq\frac{6x}{6}\)
Simplifying, we get \(-7\geq x\) or \(x\leq - 7\)

Answer:

\(x > 6\)

Problem 4: Solve \(\boldsymbol{-3\geq6x + 39}\)