Question

problem answer # problem

1 0 > 3x - 3 - 6 x 9 3(6b - 1) > 18 - 3b
2 4x + 1 - 1 ≥ -8 x 10 26 + m ≥ 5(-6 + 3m)
3 -1 ≤ 2n + 4 - 5 x 11 20 - 2p > -2( p + 2) + 4p
4 -6 > 5n + 5 + 4 x 12 x + 1 + 1 + 6x > 3(x - 4) - (x - 4)
5 7 < -(-k - 3) + 2 x
6 3 - 2(n - 4) > -1 x
7 -2(b + 1) + 4 < 10 x
8 a - 15 > -4(-6 + 3a) x

Explanation:

Problem 1: \( 0 > 3x - 3 - 6 \)

Step 1: Simplify the inequality

Simplify the right - hand side: \( 3x-3 - 6=3x-(3 + 6)=3x - 9 \). So the inequality becomes \( 0>3x - 9 \).

Step 2: Add 9 to both sides

Add 9 to both sides of the inequality: \( 0 + 9>3x-9 + 9 \), which simplifies to \( 9>3x \).

Step 3: Divide by 3

Divide both sides of the inequality by 3: \( \frac{9}{3}>\frac{3x}{3} \), so \( 3>x \) or \( x < 3 \).

Step 1: Simplify the left - hand side

Simplify \( 4x + 1-1 \), the 1 and - 1 cancel out, so we get \( 4x\geq - 8 \).

Step 2: Divide by 4

Divide both sides of the inequality by 4: \( \frac{4x}{4}\geq\frac{-8}{4} \), so \( x\geq - 2 \).

Step 1: Simplify the right - hand side

Simplify \( 2n+4 - 5=2n-(5 - 4)=2n - 1 \). So the inequality becomes \( -1\leq2n - 1 \).

Step 2: Add 1 to both sides

Add 1 to both sides: \( -1 + 1\leq2n-1 + 1 \), which gives \( 0\leq2n \).

Step 3: Divide by 2

Divide both sides by 2: \( \frac{0}{2}\leq\frac{2n}{2} \), so \( 0\leq n \) or \( n\geq0 \).

Answer:

\( x < 3 \)

Problem 2: \( 4x + 1-1\geq - 8 \)