Core Connections Integrated 1
Core Connections Integrated 1
2nd Edition
Brian Hoey, Judy Kysh, Leslie Dietiker, Tom Sallee
ISBN: 9781603283236
Table of contents
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Page 688: Closure Activity

Exercise 101
Step 1
1 of 3
#### (a)

Copied Expression Mat is on the following picture:Exercise scan

Step 2
2 of 3
#### (b)

An expression for the tiles as they appear is following:

$$
x+x-x+1+1+1-1-(x-x+1+1-1)
$$

#### (c)

Circled all of the zeos that we can find to simplify the expression are:

$$
x+boxed{x-x}+1+1+boxed{1-1}-(boxed{x-x}+1+boxed{1-1})
$$

#### (d)

The completely simplified expression is following:

$$
x+1
$$

Result
3 of 3
(a) You can use online tile algebra tools; (b) $x+x-x+1+1+1-1-(x-x+1+1-1)$; (c) $4$ groups; (d) $x+1$
Exercise 102
Step 1
1 of 2
Expression on the left side is:

$$
x+x+1+1+1-1-(x+x-1-1)=4
$$

Expression on the right side is:

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

Conclusion is that $4>3$, so, expression on the left side is greater.

Result
2 of 2
Expression on the left side is greater
Exercise 103
Step 1
1 of 3
$$
{color{#4257b2}text{a)}}
$$

$$
begin{align*}
3+7x-left(2+9xright)& {=}quad : 3+7x-2-9x\
&=7x-9x-2+3\
&=-2x-2+3\
&={color{#c34632}-2x+1}
end{align*}
$$

Step 2
2 of 3
$$
{color{#4257b2}text{b)}}
$$

$$
begin{align*}
6-left(3x-4right)+7x-11& {=}quad : 6-3x+4+7x-11\
&=-3x+7x+4+6-11\
&=4x+4+6-11\
&={color{#c34632}4x-1}
end{align*}
$$

Result
3 of 3
$$
color{#4257b2} text{ a) }-2x+1
$$

$$
color{#4257b2} text{ b) }4x-1
$$

$$
text{ }
$$

$$
text{ }
$$

$$
text{ }
$$

$$
text{ }
$$

$$
text{ }
$$

Exercise 104
Step 1
1 of 2
We need to simplify each expression below:

$$
color{#4257b2}text{(a)} 6^2-(5-4)+2(8-2^2)+8
$$

Evaluate the exponent as follows:

$$
36-(5-4)+2(8-4)+8
$$

Simplify the expression as follows:

$$
36-1+(2cdot4)+8
$$

Multiply from the left the the right as follows:

$$
36-1+8+8 text{Simplify} =51
$$

$$
color{#4257b2}text{(b)} dfrac{2(9-6)^2}{18}
$$

Evaluate the exponent as follows:

$$
dfrac{2(3)^2}{18}=dfrac{2cdot9}{18}
$$

Multiply from the left the the right as follows:

$$
dfrac{18}{18}=1
$$

Result
2 of 2
$$
text{color{#4257b2}(a) $51$ (b) $1$}
$$
Exercise 105
Step 1
1 of 2
We need to evaluate the following expression.

$$
color{#4257b2}6x-(3y+7)-xy text{When} x=5, y=3
$$

Substitute the values of $x$ and $y$ as follows:

$$
(6 cdot 5)-[(3 cdot3)+7]-(5 cdot3)
$$

Multiply from the left to the right to simplify as follows:

$$
30-(9+7)-15=30-16-15
$$

Simplify as follows:

$$
30-31=-1
$$

Result
2 of 2
$$
text{color{#4257b2}Large$-1$}
$$
Exercise 106
Step 1
1 of 2
$$
begin{align*}
& text{Group like terms}\
&3x^2-8x^2+4x-y^2+y^2-5y+10-8+3\\
&= -5x^2+4x-y^2+y^2-5y+10-8+3 tag{Add similar elements} \
&= -5x^2+4x-5y+10-8+3 tag{Add similar elements} \
&=boxed{{color{#c34632} -5x^2+4x+5-5y } }
end{align*}
$$
Result
2 of 2
$$
color{#4257b2} text{}-5x^2+4x+5-5y
$$
Exercise 107
Step 1
1 of 2
We need to Simplify the following expression an evaluate it at the given values.

$$
color{#4257b2}3x^2-5x-4+xy-(2xy+2x^2) text{When} x=-1, y=6
$$

$$
3x^2-5x-4+xy-2xy-2x^2
$$

Add tiles to groups like terms as follows:

$$
(3x^2-2x^2)+-5x+(xy-2xy)-4
$$

$$
x^2-5x-xy-4
$$

Substitute the values of $x=-1, y=6$ in the function as follows:

$$
(-1)^2-(5cdot-1)-(-1cdot6)-4=1-(-5)-(-6)-4=1+5+6-4=8
$$

Result
2 of 2
$x^2-5x-xy-4=8$
Exercise 108
Step 1
1 of 2
$$
begin{align*}
&text{Expand}\
&-3x+6=2x-9\\
&-3x+6-6=2x-9-6 tag{Subtract 6 from both sides} \
&-3x=2x-15 tag{Simplify}\
&-3x-2x=2x-15-2x tag{Subtract 2x from both sides}\
&-5x=-15 tag{Simplify}\
&frac{-5x}{-5}=frac{-15}{-5} tag{Divide both sides by -5}\\
&boxed{{color{#c34632} x=3 } }
end{align*}
$$

$$
begin{align*}
&text{We check the given equation}\
&2-(3* 3-4)=2*3-9\\
&2-5=6-9 tag{Simplify} \
&-3=-3 tag{Simplify}\
end{align*}
$$

$$
color{#965501} text{This equation is correct}
$$

Result
2 of 2
$$
color{#4257b2} text{} x=3
$$
Exercise 109
Step 1
1 of 2
We need to solve the following equations as follows:

$$
color{#4257b2}text{(a)} 1-2-(-2x)=-3-x-(2+x)
$$

Change subtraction to adding the opposite as follows:

$$
1-2+2x=-3-x-2-x
$$

Isolate the variables on the left side as follows:

$$
2x+x+x=-3-2+2-1 4x=-4
$$

$$
x=dfrac{-4}{4} x=-1
$$

$text{color{#4257b2}Check:}$ substitute the value of $x=dfrac{1}{2}$ in the equation as follows:

$$
1-2-(-2cdot-1)=-3-(-1)-(2+(-1)) 1-2-(2)=-3+1-(2-1)
$$

$$
1-2-2=-3+1-2+1 -3=-3
$$

Since the left side is equal the right side, so the answer is correct.

$$
color{#4257b2}text{(b)} 1-3-x-(3-1)=x-1-x-(3+x)
$$

Change subtraction to adding the opposite as follows:

$$
1-3-x-3+1=x-1-x-3-x
$$

Isolate the variables on the left side as follows:

$$
-x-x+x+x=-1-3-1+3+3-1 -2x+2x=-6+6
$$

$$
0=0 text{No solution}
$$

Result
2 of 2
(a) $x=-1$ (b) No solution
Exercise 110
Step 1
1 of 2
We need to solve the following equations as follows:

$$
color{#4257b2}text{(a)} -2x+2=-8
$$

Isolate the variables on the left side as follows:

$$
-2x=-8-2 -2x=-10
$$

Divided both sides of equation by $-2$ as follows.

$$
left(dfrac{-2}{-2}right) x=dfrac{-10}{-2} x=5
$$

$text{color{#4257b2}Check:}$ substitute the value of $x=5$ in the equation as follows:

$$
(-2cdot5)+2=-8 -10+2=-8 -8=-8
$$

Since the left side is equal the right side, so the answer is correct.

$$
color{#4257b2}text{(b)} 4x-2+x=2x+8+3x
$$

Isolate the variables on the left side as follows:

$$
4x+x-2x-3x=8+2 5x-5x=10
$$

$$
0=10 text{No solution}
$$

Result
2 of 2
(a) $x=5$ (b) No solution
Exercise 111
Step 1
1 of 2
You can check your answers using the table at the end of the closure section. There you can see do you have problems with some kind of tasks and use the table to make a list of topics you need help.
Result
2 of 2
Use the table at the end of the closure section
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Chapter 2: Linear Functions
Page 53: Questions
Page 109: Closure Activity
Chapter 3: Transformations and Solving
Page 115: Questions
Page 186: Closure Activity
Chapter 5: Sequences
Page 247: Questions
Page 297: Closure Activity
Chapter 6: Systems of Equations
Page 303: Questions
Page 359: Closure Activity
Chapter 7: Congruence and Coordinate Geometry
Page 365: Questions
Page 420: Closure Activity
Chapter 8: Exponential Functions
Page 429: Questions
Page 487: Closure Activity
Chapter 10: Functions and Data
Chapter 11: Constructions and Closure
Page 585: Questions
Page 634: Closure Activity