Question

1. solve the following equation. |x - 3|+8 = 15
2. solve the inequality. graph its solution. 7(3p + 6)+4≥172
3. solve the inequality. graph its solution.

\\(\frac{|6a|}{6}>3\\)
e a < - 6 or a > 4:
g - 3 < a < 3:
h - 6 < a < 4:
j a > 3 or a < - 3:

Explanation:

7. Solve the equation \(|x - 3|+8 = 15\)

Step1: Isolate the absolute - value term

Subtract 8 from both sides of the equation \(|x - 3|+8 = 15\).
\(|x - 3|=15 - 8=7\)

Step2: Set up two cases

Case 1: \(x−3 = 7\). Solve for \(x\): \(x=7 + 3=10\).
Case 2: \(x−3=-7\). Solve for \(x\): \(x=-7 + 3=-4\).

9. Solve the inequality \(7(3p + 6)+4\geq172\)

Step1: Expand the left - hand side

Use the distributive property: \(7(3p + 6)+4=21p+42 + 4=21p+46\).
So the inequality becomes \(21p+46\geq172\).

Step2: Isolate the variable term

Subtract 46 from both sides: \(21p\geq172 - 46=126\).

Step3: Solve for \(p\)

Divide both sides by 21: \(p\geq\frac{126}{21}=6\).

10. Solve the inequality \(\frac{|6a|}{6}>3\)

Step1: Simplify the left - hand side

\(\frac{|6a|}{6}=|a|\), so the inequality is \(|a|>3\).

Step2: Set up two cases

Case 1: \(a>3\).
Case 2: \(a < - 3\). This is because for \(|a|>k\) (\(k>0\)), the solution is \(a>k\) or \(a < - k\).

Answer:

\(x = 10\) or \(x=-4\)