Question

algebra post test for incoming freshmen (a)
name: haileese robinson date: 6-30-20
directions: answer all 24 questions. show all work. use the back of the page if needed.

write a variable expression for each situation.

1. the sum of a number and 8
2. five times a number decreased by 12
3. the quotient of a number and 3, increased by 7

simplify each expression. show your work.

1. \\(3x + 5x - 2\\)
2. \\(7a - 3a + 4b + 2b\\)
3. \\(x^2 + 3x - 5 + x^2 - x + 1\\)
4. \\(4m + 3n - 2m + 5n\\)

solve each equation.

1. \\(2x + 5 = 13\\)

Explanation:

Write variable expressions

Let \(n\) represent the unknown number.

1. "The sum of a number and 8":

\(n + 8\)

1. "Five times a number decreased by 12":

\(5n - 12\)

1. "The quotient of a number and 3, increased by 7":

\(\frac{n}{3} + 7\)

Simplify each expression

Combine like terms.

1. \(3x + 5x - 2 = (3+5)x - 2 = 8x - 2\)
2. \(7a - 3a + 4b + 2b = (7-3)a + (4+2)b = 4a + 6b\)
3. \(x^2 + 3x - 5 + x^2 - x + 1 = (1+1)x^2 + (3-1)x + (-5+1) = 2x^2 + 2x - 4\)
4. \(4m + 3n - 2m + 5n = (4-2)m + (3+5)n = 2m + 8n\)

Solve each equation

Isolate the variable.

1. \(2x + 5 = 13 \implies 2x = 8 \implies x = 4\)

Answer:

No.	Problem	Answer
2	Five times a number decreased by 12	\(5n - 12\)
3	The quotient of a number and 3, increased by 7	\(\frac{n}{3} + 7\)
4	\(3x + 5x - 2\)	\(8x - 2\)
5	\(7a - 3a + 4b + 2b\)	\(4a + 6b\)
6	\(x^2 + 3x - 5 + x^2 - x + 1\)	\(2x^2 + 2x - 4\)
7	\(4m + 3n - 2m + 5n\)	\(2m + 8n\)
8	\(2x + 5 = 13\)	\(x = 4\)