Translate the following phrases into algebraic expressions and represent the given inequality on a number…

Question

Translate the following phrases into algebraic expressions and represent the given inequality on a number line.

ScanSolve AI Tutor · Accepted Answer

Here are the algebraic expressions for statements D and E, and the number line representation for Question 2, Part A:

D) The sum of $x$ and $y$ cubed.

Identify the term "y cubed".
$y^3$
Find the sum of $x$ and $y^3$ .
$\boxed{x + y^3}$
E) The amount by which $x$ exceed $y$ cubed.
Identify the term "y cubed".
$y^3$
Express the amount by which $x$ exceeds $y^3$ as a difference.
$\boxed{x - y^3}$
Indicate the region of the number line that represents the following.

A) $x \ge -1$ AND $x < 6$
Understand the first inequality, $x \ge -1$ .
This means $x$ is greater than or equal to -1. On a number line, this is represented by a solid dot at -1 and shading to the right.
Understand the second inequality, $x < 6$ .
This means $x$ is less than 6. On a number line, this is represented by an open dot at 6 and shading to the left.
Combine the inequalities using "AND".
The "AND" condition means that $x$ must satisfy both inequalities simultaneously. The region where both are true is between -1 (inclusive) and 6 (exclusive).

Number line representation:
Draw a number line. Place a solid dot (•) at -1. Place an open dot (○) at 6. Shade the region between -1 and 6.
$\text{<---•------------------○--->}$ $\quad \quad \text{-1} \quad \quad \quad \quad \quad \text{6}$

Translate the following phrases into algebraic expressions and represent the given inequality on a number line.