1
Question 1 of 10
Not answered
Solve for x: x + 9 = 16
Hint: Subtract 9 from both sides.
Explanation: Subtract 9 from both sides: x = 16 - 9 = 7.
Algebra quiz
Equations and Inequalities Quiz
Practice solving linear equations, two-step equations, inequalities, equations with parentheses, and equations with variables on both sides. Use hints when needed, choose an answer, and review the explanation after each question.
2
Question 2 of 10
Not answered
Solve for x: 4x = 28
Hint: Divide both sides by 4.
Explanation: Divide both sides by 4: x = 28 ÷ 4 = 7.
3
Question 3 of 10
Not answered
Solve for x: 3x - 5 = 16
Hint: First add 5 to both sides, then divide by 3.
Explanation: Add 5 to both sides: 3x = 21. Divide by 3, so x = 7.
4
Question 4 of 10
Not answered
Solve for x: 2(x + 4) = 18
Hint: Divide both sides by 2 first, then subtract 4.
Explanation: Divide by 2: x + 4 = 9. Subtract 4 from both sides: x = 5.
5
Question 5 of 10
Not answered
Solve for x: 5x + 3 = 2x + 18
Hint: Move the x-terms to one side and constants to the other side.
Explanation: Subtract 2x from both sides: 3x + 3 = 18. Subtract 3: 3x = 15. Divide by 3, so x = 5.
6
Question 6 of 10
Not answered
Solve the inequality: x - 4 > 10
Hint: Add 4 to both sides.
Explanation: Add 4 to both sides: x > 14.
7
Question 7 of 10
Not answered
Solve the inequality: 2x ≤ 12
Hint: Divide both sides by 2. The inequality sign stays the same because 2 is positive.
Explanation: Divide both sides by 2: x ≤ 6.
8
Question 8 of 10
Not answered
Solve the inequality: -3x > 9
Hint: When dividing by a negative number, reverse the inequality sign.
Explanation: Divide both sides by -3 and reverse the sign: x < -3.
9
Question 9 of 10
Not answered
Solve for x: (x / 5) + 2 = 9
Hint: First subtract 2, then multiply by 5.
Explanation: Subtract 2 from both sides: x/5 = 7. Multiply by 5, so x = 35.
10
Question 10 of 10
Not answered
Solve for x: 7 - 2x = 15
Hint: Subtract 7 from both sides first. Be careful with the negative coefficient.
Explanation: Subtract 7 from both sides: -2x = 8. Divide by -2, so x = -4.
Your result
You answered 0 out of 10 questions correctly.
Equations vs inequalities
The algebraic moves are similar, but the meaning of the answer is different
This quiz mixes linear equations with inequalities. In an equation, you usually isolate one value of x that makes two expressions equal. In an inequality, the result usually describes an entire interval of values.
=
Equation
Example: 3x − 5 = 16. Solving gives x = 7. The solution is a specific value that makes the two sides equal.
>
Inequality
Example: x − 4 > 10. Solving gives x > 14. Every number greater than 14 belongs to the solution set.
Inequality number line
Why dividing by a negative reverses the inequality
Start with −3x > 9. Dividing both sides by −3 gives x < −3. The direction reverses because multiplication by a negative reflects numbers across zero and reverses their order.
−3
The endpoint is open because −3 itself does not satisfy the strict inequality. The shaded direction extends left because the solutions are numbers smaller than −3.
Boundaries matter
Strict and inclusive inequalities describe different solution sets
The symbols < and > exclude the boundary value, while ≤ and ≥ include it. That difference affects both the number-line graph and whether the endpoint itself is a solution.
14 is only the boundary. It is not part of the solution set because the inequality is strict.
Open circle = boundary excluded
6 is included because the symbol contains equality. Values smaller than 6 also satisfy the inequality.
Closed circle = boundary included
Test-point check
Verify an inequality with values from both sides of the boundary
For x < −3, try one value that should work and one that should fail in the original inequality −3x > 9.
x = −4
−3(−4) = 12, and 12 > 9 is true. So −4 belongs to the solution set.
x = −2
−3(−2) = 6, and 6 > 9 is false. So −2 does not belong to the solution set.
x = −3
−3(−3) = 9. Because 9 > 9 is false, the boundary value is excluded.
Harder comparison
Combine parentheses, variables on both sides, and an inequality
A stronger high-school example is 4(2x − 3) ≤ 5x + 9. The solving process looks like an equation until the final result is interpreted as an interval.
8x − 12 ≤ 5x + 9
3x − 12 ≤ 9
3x ≤ 21
x ≤ 7
Common mistakes
Three errors that are especially important in equations and inequalities
Reversing the sign when you should not
Adding or subtracting the same quantity does not reverse an inequality. Neither does dividing by a positive number.
2x ≤ 12 → x ≤ 6. The sign stays the same.
Forgetting to reverse after a negative
Dividing by a negative reverses the ordering relationship, even when the arithmetic itself is simple.
−3x > 9 → x < −3.
Treating an inequality answer as one number
The boundary is not usually the whole answer. An inequality describes all values on one side of that boundary.
x > 14 means 15, 20, 100, 14.1, and infinitely many other values.
Use your result
What to review after this 10-question set
0–4 correct
Review inverse operations and basic linear equations first. Then return to simple inequalities with positive coefficients.
5–7 correct
Focus on the question types you missed: variables on both sides, negative coefficients, or interpreting ≤ and ≥ correctly.
8–10 correct
Move to multi-step inequalities, compound inequalities, absolute-value inequalities, and more contextual problems.
Continue practicing