Question

1. 2x - 3 < x + 3 and -10 + 6x ≤ 7x + 5
2. -10v - 6 > 6v + 10 or v + 5 ≤ 6v + 5
3. 10n + 8 < 5n - 7 and 5 + 4n ≤ 5n + 9

Explanation:

Step1: Solve the first inequality in 10)

Solve \(2x - 3

Step2: Solve the second - inequality in 10)

Solve \(-10 + 6x\leq7x + 5\). Subtract \(6x\) from both sides and subtract 5 from both sides: \(-10-5\leq7x-6x\), so \(x\geq - 15\).
The solution for 10) is \(-15\leq x<6\).

Step3: Solve the first inequality in 12)

Solve \(-10v-6>6v + 10\). Add \(10v\) to both sides: \(-6>16v + 10\). Then subtract 10 from both sides: \(-16>16v\). Divide both sides by 16: \(v<-1\).

Step4: Solve the second - inequality in 12)

Solve \(v + 5\leq6v+5\). Subtract \(v\) from both sides and subtract 5 from both sides: \(0\leq5v\), so \(v\geq0\).
The solution for 12) is \(v<-1\) or \(v\geq0\).

Step5: Solve the first inequality in 14)

Solve \(10n + 8<5n-7\). Subtract \(5n\) from both sides and subtract 8 from both sides: \(10n-5n<-7 - 8\), so \(5n<-15\), and \(n<-3\).

Step6: Solve the second - inequality in 14)

Solve \(5 + 4n\leq5n + 9\). Subtract \(4n\) from both sides and subtract 9 from both sides: \(5 - 9\leq5n-4n\), so \(n\geq - 4\).
The solution for 14) is \(-4\leq n<-3\).

Answer:

1. \(-15\leq x<6\)
2. \(v<-1\) or \(v\geq0\)
3. \(-4\leq n<-3\)