Targeted Review Solutions

Simplify. Answers should contain positive exponents only.

$\frac{x^{3} y^{- 2}}{y^{2} x^{4}}$

$\frac{1}{x^{4 - 3} y^{2 - (- 2)}}$

$\frac{1}{x y^{4}}$

Note

Use the Formula Sheet to review the exponent rules.

${(3 p^{2} q^{- 5})}^{2}$

$3^{2} p^{2 \cdot 2} q^{- 5 \cdot 2}$

$\frac{9 p^{4}}{q^{10}}$

Multiply.

$(x - 3) (5 x + 1)$

$5 x^{2} + x - 15 x - 3$

$5 x^{2} - 14 x - 3$

$(2 x + 3) (x^{2} - 4 x - 5)$

$2 x^{3} - 8 x^{2} - 10 x + 3 x^{2} - 12 x - 15$

$2 x^{3} - 5 x^{2} - 22 x - 15$

Note

Before combining like terms, you should have 6 terms because (2)(3) = 6.

Factor.

$25 x^{2} y^{2} + 15 x y^{2} + 30 x y$

$5 x y (5 x y + 3 y + 6)$

Note

Remember to look for the greatest common factor (GCF) first.

$8 x (x + 11) - 6 (x + 11)$

$(x + 11) (8 x - 6)$

Note

This can be factored by finding the common binomial, (x + 11).

Solve.

$\frac{2}{3} x - 5 = \frac{1}{6}$

$\begin{array}{rcl} (6) (\frac{2}{3} x - 5 & = & \frac{1}{6}) \\ 4 x - 30 & = & 1 \\ 4 x & = & 31 \end{array}$

$x = \frac{31}{4}$

Note

Multiply every term on both sides by the LCD, 6, to clear the fractions from the equation.

$9 (x - \frac{2}{3}) + 2 x = 6 (2 x + 1)$

$\begin{array}{rcl} 9 x - 6 + 2 x & = & 12 x + 6 \\ 11 x - 6 & = & 12 x + 6 \end{array}$

$x = - 12$

Multiple Choice

Select all terms that are like terms.

$3 x^{3}$
3x
$x^{3}$
3

Note

Like terms have the same base raised to the same power. Like terms can have different coefficients.

Solve:
$| 4 x + 3 | > 5$

Note

Has the correct endpoint but does not change the direction of the inequality symbol in case 2
Represents an AND compound inequality

Has the solution for case 1, but not case 2

$\begin{array}{rcl} Case 1 OR Case 2 \\ 4 x + 3 & > & 5 OR - (4 x + 3) > 5 \\ 4 x & > & 2 4 x + 3 > - 5 \\ x & > & \frac{1}{2} 4 x < - 8 \\ x < - 2 \end{array}$

Select all solutions to the equation $4 x^{2} = 64 .$

– 4
4
± 4
± 8

Note

± 8 would be the solution if both sides are not divided by four first.

$x^{2} = 16 x^{2} - 16 = 0 (x + 4) (x - 4) = 0 x = \pm 4$

Bob did chores for his neighbor. He already has $8 saved. Then he earned $10 per day for two weeks. If he took off one day each week, how much did he save at the end of two weeks?

$18
$68
$128
$148

Note

This is the sum of the first and second day only.
This is the sum of the first day and one week.

This is the solution when taking a day off is ignored.

$Total = first day + 2 weeks ($ 10 \cdot 6 days a week) Total = 8 + 2 (10 \cdot 6) = 128$

Problem	1	2	3	4	5	6	7	8	9	10	11	12
Origin	A1	A1	A1	A1	A1	A1	A1	A1	A1	A1	A1	A1

L = Lesson in this level, A1 = Algebra 1: Principles of Secondary Mathematics, FD = Foundational Knowledge