Chapter 1: Foundations

Why is it important to use the order of operations to simplify an expression?

Explain how you identify the like terms in the expression$8a^2+4a+9-a^2-1$.

Explain the difference between the phrases “4 times the sum ofx and y” and “the sum of 4 times x and y”.

In the following exercises, fill in $<$, $>$, or $=$for each of the following pairs of numbers.

(a) role="math" localid="1644153225528" $\left|-7\right|\_\_\_-\left|-7\right|$

(b) role="math" localid="1644153205707" $6\_\_\_-\left|-6\right|$

(c) role="math" localid="1644153174235" $\left|-11\right|\_\_\_-11$

(d)$-\left(-13\right)\_\_\_-\left|-13\right|$

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

39,075

In the following exercises, fill in $<$, $>$, or $=$for each of the following pairs of numbers.

(a) role="math" localid="1644156564186" $-\left|-9\right|\_\_\_\left|-9\right|$

(b) role="math" localid="1644156529789" $-8\_\_\_\left|-8\right|$

(c) role="math" localid="1644156507272" $\left|-1\right|\_\_\_-1$

(d)$-\left(-14\right)\_\_\_-\left|-14\right|$

In the following exercises, fill in $<$, $>$, or $=$for each of the following pairs of numbers.

(a) role="math" localid="1644160885161" $-\left|2\right|\_\_\_-\left|-2\right|$

(b) role="math" localid="1644160856233" $-12\_\_\_-\left|-12\right|$

(c) role="math" localid="1644160846883" $\left|-3\right|\_\_\_-3$

(d)$\left|-19\right|\_\_\_-\left(-19\right)$

In the following exercise, fill in $<$, $>$, or $=$for each of the following pairs of numbers.

(a) role="math" localid="1644163324487" $-\left|-4\right|\_\_\_-\left|4\right|$

(b) role="math" localid="1644163316022" $5\_\_\_-\left|-5\right|$

(c) $-\left|-10\right|\_\_\_-10$

(d)role="math" localid="1644163275509" $-\left|-0\right|\_\_\_-\left(-0\right)$

In the following exercises, simplify.

$\left|15-7\right|-\left|14-6\right|$

In the following exercises, simplify.

$|17-8|-|13-4|$