?> Real Number System Worksheet | Problems & Solutions

# Real Number System Worksheet

Real Number System Worksheet
• Page 1
1.
Convert interval notation [- 2, 4) to inequality notation.
 a. 2 ≤ $x$ ≤ 4 b. - 2 ≤ $x$ < 4 c. - 2 < $x$ < 4 d. - 2 ≤ $x$ ≤ 4

#### Solution:

The interval [- 2, 4) corresponds to - 2 ≤ x < 4.

2.
Convert interval notation [- 2, 2] to inequality notation.
 a. - 2 ≤ $x$ ≤ 2 b. - 2 < $x$ < 2 c. - 2 > $x$ > 2 d. - 2 ≤ $x$ < 2

#### Solution:

The interval [- 2, 2] corresponds to - 2 ≤ x ≤ 2.

3.
Find the end points of the interval [- 4, 3).
 a. - 4 & 3 b. - 3 & ∞ c. - ∞, ∞ d. - ∞ & 4

#### Solution:

The end points of the interval [- 4, 3) are - 4 & 3.

4.
Convert the inequality - 3 ≤ $x$ ≤ 3 to interval notation.
 a. [- 3, 3] b. (- 3, 3) c. [3, 3] d. [3, 3)

#### Solution:

The corresponding interval notation for the given inequality is [- 3, 3].

5.
Convert the inequality - 3 ≤ $x$ < 6 to interval notation.
 a. [3, 6) b. (3, 6) c. (- 3, 6) d. [- 3, 6)

#### Solution:

The interval notation for the given inequality is [- 3, 6).

6.
Write the expanded form of ($c$ + $x$)$z$.
 a. $\mathrm{xzc}$ b. $\mathrm{cz}$ + $\mathrm{xz}$ c. $\mathrm{cx}$ - $\mathrm{xz}$ d. $\mathrm{cx}$ + $\mathrm{xz}$

#### Solution:

(c + x)z = cz + xz
[Use distributive property.]

7.
Write the expanded form of 3($x$ - 2).
 a. 3$x$ - 6 b. 3$x$ + 6 c. 3$x$ d. 3$x$ - 2

#### Solution:

3(x - 2) = 3x - 6
[Use distributive property.]

8.
The base of the exponential expression ${\left(8\right)}^{45}$ is ____.
 a. 53 b. 45 c. 8 d. 37

#### Solution:

The base of the exponential expression (8)45 is 8.

9.
The exponent of the exponential expression (3)-3 is
 a. 3 b. - 3 c. 10 d. 6

#### Solution:

The exponent of the exponential expression (3)-3 is - 3.

10.
Simplify: $\frac{5y{z}^{10}}{{y}^{4}{z}^{5}}$
 a. 5$\mathrm{yz}$ b. 5 $\frac{y}{z}$ c. 5 $\frac{{z}^{5}}{{y}^{3}}$ d. 5 $\frac{{y}^{5}}{{z}^{3}}$

#### Solution:

5yz10y4z5 = 5 (y1 - 4)(z10 - 5)
[Use aman=am-n.]

= 5 (y -3)(z 5)

= 5 z5y3