Math Problem Statement

3π‘Ž βˆ’ 2 β‰₯ 8

Solution

To solve the inequality 3aβˆ’2β‰₯83a - 2 \geq 8, follow these steps:

  1. Add 2 to both sides of the inequality to isolate the term with aa: 3aβˆ’2+2β‰₯8+23a - 2 + 2 \geq 8 + 2 3aβ‰₯103a \geq 10

  2. Divide both sides by 3 to solve for aa: aβ‰₯103a \geq \frac{10}{3} aβ‰₯3.333β€Ύa \geq 3.33\overline{3}

So, the solution to the inequality is: aβ‰₯103a \geq \frac{10}{3}

Would you like any further details or clarification on this process?

Here are some related questions you can try:

  1. Solve 4x+5≀3x+124x + 5 \leq 3x + 12.
  2. Solve 2bβˆ’7>92b - 7 > 9.
  3. Solve 5y+3<125y + 3 < 12.
  4. Solve a2βˆ’4β‰₯1\frac{a}{2} - 4 \geq 1.
  5. Solve 3p+6>153p + 6 > 15.

Tip: Always perform the same operation on both sides of an inequality to keep it balanced.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Inequalities

Formulas

Basic linear inequality solving rules

Theorems

Transposition
Division Property of Inequality

Suitable Grade Level

Grades 7-8