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Intermediate Algebra Daily Practice
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Intermediate Algebra Daily Practice
Simplify and solve carefully. Show your reasoning where requested.
Number Sense and Operations
1.Evaluate: −5/8 + 3/4.
2.Evaluate: (−3)³ ÷ 9.
3.Evaluate: √169 − 3².
4.Select every rational number.
- √16
- √7
- 0.625
- π
- −11/4
5.The number line shows four values. Write them in order from least to greatest.
6.List all positive factors of 54, then find the greatest common factor of 54 and 72.
7.Which expression is equivalent to 5⁻¹ × 5⁴?
- 5⁻⁴
- 5³
- 25³
- 5⁵
Simplifying and Solving
8.Combine like terms: 7x² + 2x − 5 − 3x² + 6x + 8.
9.Simplify: 4(2x − 3) − (3x + 5).
10.Solve for x: 7x + 4 = 3x + 28. Show your steps.
11.Solve for x: x/5 − 2 = 4.
12.Two positive integers have a greatest common factor of 6 and a least common multiple of 84. One integer is 12. Find the other integer and show how you know.
13.A rectangular display sign at a local bakery is 2x + 7 inches long and 5 inches wide. Write a simplified expression for its perimeter. Then find the perimeter when x = 4.
Concept Check
14.Match each algebraic phrase to its expression.
- Seven less than twice a number n
- The quotient of a number p and 4
- Five added to the square of t
- Three times the sum of a and 2
- 3(a + 2)
- 2n − 7
- t² + 5
- p/4
15.A student claims that √25 + √49 equals √74 because 25 + 49 = 74. Is the claim correct? Explain using the values of the square roots.
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