Algebra Practice Problems

Comprehensive algebra practice covering everything from basic expressions to systems of equations. Build a strong foundation in algebraic thinking with these carefully designed problems.

Grades 7-10Key Stage 3-4Årskurs 7 - Gymnasiet

Skills You'll Practice

Simplifying algebraic expressions
Evaluating expressions
Solving equations and inequalities
Working with exponents
Understanding functions
Graphing linear equations
Solving systems of equations

Expressions & Simplifying

Easy

Simplify: 3x + 5x - 2x

💡 Show Hint

Combine like terms

✓ Show Answer

Evaluate 2x + 5 when x = 4

💡 Show Hint

Substitute 4 for x: 2(4) + 5

✓ Show Answer

Simplify: 4(x + 3)

💡 Show Hint

Distribute the 4

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4x + 12

Equations & Inequalities

Medium

Solve: 5x - 3 = 2x + 12

💡 Show Hint

Get all x terms on one side

✓ Show Answer

x = 5

Solve: -2x + 7 > 15

💡 Show Hint

Divide by -2, flip the inequality sign!

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x < -4

Solve: |x - 3| = 5

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x - 3 = 5 OR x - 3 = -5

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x = 8 or x = -2

Systems & Functions

Hard

Solve the system: y = 2x + 1 and y = -x + 7

💡 Show Hint

Set 2x + 1 = -x + 7

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(2, 5)

If f(x) = x² - 4x, find f(5)

💡 Show Hint

f(5) = 25 - 20

✓ Show Answer

What is the slope and y-intercept of 3x - 2y = 8?

💡 Show Hint

Rewrite in y = mx + b form

✓ Show Answer

slope = 3/2, y-intercept = -4

Pro Tips

💡Like terms have the same variable AND the same exponent
💡When multiplying/dividing an inequality by a negative, flip the sign
💡For systems of equations, substitution or elimination both work—choose wisely
💡Function notation f(x) just means "plug x into the function"

Curriculum Alignment

CommonCore (7.EE)CommonCore (8.EE)CommonCore (HSA)

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