The AI Algebra Solver specializes in solving and explaining the following algebra topics:

Representing Numbers by Letters: Understanding variables, coefficients, and constants.

Solving Equations: Linear, quadratic, and other algebraic equations.

Working with Inequalities: Solving and graphing inequalities.

Operations with Polynomials: Adding, subtracting, multiplying, and dividing polynomials.

Factoring: Factoring quadratic and higher-degree polynomials.

Expanding Expressions: Using distributive properties to expand brackets.

Graphing Equations: Plotting and analyzing graphs of linear and quadratic equations.

Systems of Equations: Solving systems of linear equations.

Examples Solved by AI Algebra Solver

1. Representing Numbers by Letters

Problem: Write the algebraic expression for “three times a number increased by five.”
Solution:
1. Let the number be \(x\).
2. “Three times a number” is \(3x\).
3. “Increased by five” means \(3x + 5\).
Answer: \(3x + 5\).

2. Solving Linear Equations

Problem: Solve \(2x – 7 = 13\).
Solution:
1. Add 7 to both sides: \(2x = 20\).
2. Divide by 2: \(x = 10\).
Answer: \(x = 10\).

3. Working with Inequalities

Problem: Solve \(4x + 3 > 15\).
Solution:
1. Subtract 3 from both sides: \(4x > 12\).
2. Divide by 4: \(x > 3\).
Answer: \(x > 3\).

4. Adding Polynomials

Problem: Add \(2x^2 + 3x + 5\) and \(x^2 – 4x + 2\).
Solution:
1. Combine like terms:
– \(2x^2 + x^2 = 3x^2\),
– \(3x – 4x = -x\),
– \(5 + 2 = 7\).
Answer: \(3x^2 – x + 7\).

5. Factoring Quadratic Expressions

Problem: Factor \(x^2 + 5x + 6\).
Solution:
1. Find two numbers that multiply to 6 and add to 5: \(2\) and \(3\).
2. Rewrite as \((x + 2)(x + 3)\).
Answer: \((x + 2)(x + 3)\).

6. Expanding Brackets

Problem: Expand \((x + 2)(x – 3)\).
Solution:
1. Use the distributive property:
– \(x \cdot x = x^2\),
– \(x \cdot -3 = -3x\),
– \(2 \cdot x = 2x\),
– \(2 \cdot -3 = -6\).
2. Combine like terms: \(x^2 – x – 6\).
Answer: \(x^2 – x – 6\).

7. Solving Systems of Equations

Problem: Solve \(x + y = 10\) and \(2x – y = 5\).
Solution:
1. Add the equations to eliminate \(y\):
\[
(x + y) + (2x – y) = 10 + 5 \quad \Rightarrow \quad 3x = 15.
\]
2. Solve for \(x\): \(x = 5\).
3. Substitute \(x = 5\) into \(x + y = 10\):
\[
5 + y = 10 \quad \Rightarrow \quad y = 5.
\]
Answer: \(x = 5, y = 5\).

8. Graphing Linear Equations

Problem: Graph \(y = 2x + 1\).
Solution:
1. Find two points:
– When \(x = 0\), \(y = 1\).
– When \(x = 1\), \(y = 3\).
2. Plot the points \((0, 1)\) and \((1, 3)\).
3. Draw a straight line through them.

9. Quadratic Equations

Problem: Solve \(x^2 – 3x – 4 = 0\).
Solution:
1. Factor into \((x – 4)(x + 1) = 0\).
2. Solve each factor:
– \(x – 4 = 0 \quad \Rightarrow \quad x = 4\),
– \(x + 1 = 0 \quad \Rightarrow \quad x = -1\).
Answer: \(x = 4, x = -1\).

10. Working with Inequalities on a Graph

Problem: Graph \(y < 2x – 1\).
Solution:
1. Graph the line \(y = 2x – 1\) as a dashed line.
2. Shade the region below the line to represent \(y < 2x – 1\).