Chapter 1 Algebra: Understand Numerical And Algebraic Expressions
Guided Practice 6
Page 45 Exercise 1 Answer
The expression 2y – y can be written as y because 2y and y are like terms so we can simplify it by using Properties of Operations.
2y − y
= 2y − 1y Using Identity Property of Multiplication
= (2 − 1)y Using Distributive Property
= y
Result
Because 2y and y are like terms so we can simplify the expression
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Page 45 Exercise 2 Answer
\(\frac{1}{2}\)x + \(\frac{1}{2}\)x and x are equivalent because if we simplify the expression \(\frac{1}{2}\)x + \(\frac{1}{2}\)x we will get x
\(\frac{1}{2}\)x + \(\frac{1}{2}\)x
= (\(\frac{1}{2}\) + \(\frac{1}{2}\))x Using Distrtibutive Property
= x
Result
Because the expression \(\frac{1}{2}\)x + \(\frac{1}{2}\)x when simplify will become x
Page 45 Exercise 3 Answer
No, 4\(z^2\) − \(z^2\) and 4 are not equivalent expressions.
4\(z^2\) − \(z^2\)
= (4 − 1)\(z^2\) Using Distributive Property
= 3\(z^2\)
Result
No, 4\(z^2\) − \(z^2\) and 4 are not equivalent expressions.
Page 45 Exercise 4 Answer
x + x + x + x Given
= 1x + 1x + 1x + 1x Use Identity Property of Multiplication
= (1 + 1 + 1 + 1)x Use Distributive Property
= 4x Simplify
Result
4x
Page 45 Exercise 5 Answer
4y − y Given
= 4y − 1y Use Identity Property of Multiplication
= (4 − 1)y Use Distributive Property
= 3y Simplify
Result
3y
Page 45 Exercise 6 Answer
3x + 8 + 2x Given
= 3x + 2x + 8 Using Commutative Property of Addition
= 5x + 8 Combine like terms
Result
5x + 8
Page 45 Exercise 7 Answer
7y − 4.5 − 6y Given
= 7y − 6y − 4.5 Group like terms
= y − 4.5 Combine Like terms
Result
y − 4.5
Page 45 Exercise 8 Answer
4x + 2 − \(\frac{1}{2} x\) Given
= 4x – \(\frac{1}{2} x\) + 2 Group like terms
= \(\left(4-\frac{1}{2}\right) x+2\) Using Distributive Property
= \(3 \frac{1}{2}\)x + 2 Simplify
Result
\(3 \frac{1}{2}\)x + 2
Page 45 Exercise 9 Answer
3 + 3y − 1 + y Given
= 3y + y + 3 − 1 Group like terms
= 3y + 1y + 3 − 1 Using Identity Property of Multiplication
= (3 + 1)y + 3 − 1 Using Distributive Property
= 4y + 2 Simplify
Result
4y + 2
Page 45 Exercise 10 Answer
x + 6x Given
= 1x + 6x Using Identity Property of Multiplication
= (1 + 6)x Using Distributive Property
Step 4
= 7x Simplify
Result
7x
Page 45 Exercise 11 Answer
9y − 3y Given
= (9 − 3)y Using Distributive Property
= 6y Simplify
Result
6y
Page 45 Exercise 12 Answer
2z + \(\frac{1}{4}\) + 2z Given
= 2z + 2z + \(\frac{1}{4}\) Group like terms
= (2 + 2)z + \(\frac{1}{4}\) Using Distributive Property
= 4z + \(\frac{1}{4}\) Simplify
Result
4z + \(\frac{1}{4}\)
Page 45 Exercise 13 Answer
5 + 3w + 3 − w Given
= 5 + 3 + 3w − w Group Like terms
= 5 + 3 + 3w − 1w Using Identity Property of Multiplication
= 5 + 3 + (3 − 1)w Using Distributive Property
= 8 + 2w Simplify
Result
8 + 2w
Page 45 Exercise 14 Answer
5w − 5w Given
= (5 − 5)w Using Distributive Property
= 0 Simplify
Result
0
Page 45 Exercise 15 Answer
2x + 5 + 3x + 6 Given
= 2x + 3x + 5 + 6 Group Like Terms
= (2 + 3)x + 5 + 6 Using Distributive Property
= 5x + 11 Simplify
Result
5x + 11
Page 45 Exercise 16 Answer
10\(y^2\) + 2\(y^2\) Given
= (10 + 2)\(y^2\) Using Distributive Property
= 12\(y^2\) Simplify
Result
12\(y^2\)
Page 45 Exercise 17 Answer
\(\frac{3}{4} z^3+4-\frac{1}{4} z^3\) Given
= \(\frac{3}{4} z^3-\frac{1}{4} z^3+4\) Group Like terms
= \(\left(\frac{3}{4}-\frac{1}{4}\right) z^3+4\) Using Distributive Property
= \(\left(\frac{3-1}{4}\right) z^3+4\) LCM is 4
= \(\left(\frac{2}{4}\right) z^3+4\) Subtract
= \(\frac{1}{2} z^3+4\) Simplify
Result
\(\frac{1}{2} z^3+4\)Page 45 Exercise 18 Answer
3.4m + 2.4m Given
= (3.4 + 2.4)m Using Distributive Property
= 5.8m Simplify
Result
5.8m
Page 45 Exercise 19 Answer
4.2n + 5 − 3.2n Given
= 4.2n − 3.2n + 5 Group Like Terms
= (4.2 − 3.2)n + 5 Using Distributive Property
= n + 5 Simplify
Result
n + 5
Page 45 Exercise 20 Answer
5\(p^2\) – 5 – 2\(p^2\) Given
= 5\(p^2\) – 2\(p^2\) – 5 Group like terms
= (5 – 2)\(p^2\) – 5 Using Distributive Property
= \(3p^2\) − 5 Simplify
Result
\(3p^2\) − 5
Page 45 Exercise 21 Answer
\(q^5+q^5+q^5\) Given
= \(1 q^5+1 q^5+1 q^5\) Using Identity Property of Multiplication
= (1 + 1 + 1)\(q^5\) Using Distributive Property
= \(3q^5\) Simplify
Result
\(3q^5\)Page 45 Exercise 22 Answer
\(3 x+\frac{1}{4}+2 y+\frac{1}{4}+7 x-y\) Given
= \(3 x+7 x+2 y-y+\frac{1}{4}+\frac{1}{4}\) Group like terms
= \((3+7) x+(2-1) y+\frac{1+1}{4}\) Using Distributive Property
= 10x + y + \(\frac{2}{4}\) Simplify
= 10x + y + \(\frac{1}{2}\) Simplify
Result
10x + y + \(\frac{1}{2}\)
Page 45 Exercise 23 Answer
1.5\(z^2\) + 4.5 + 6z − 0.3 − 3z + \(z^2\) Given
= 1.5\(z^2\) + \(z^2\) + 6z − 3z + 4.5 − 0.3 Group like terms
= 1.5\(z^2\) + 1z + 6z − 3z + 4.5 − 0.3 Using Identity Property of Multiplication
= (1.5 + 1)\(z^2\) + (6 − 3)z + 4.5 − 0.3 Using Distributive Property
= 2.5\(z^2\) + 3z + 4.2 Simplify
Result
2.5\(z^2\) + 3z + 4.2
Page 46 Exercise 24 Answer
Length = 2y + 1; Width = y
Algebraic Expression:
Perimeter = 2(Length + width) = 2(2y + 1 + y)
Result
2(2y + 1 + y)
Page 46 Exercise 25 Answer
2(2y + 1 + y) Given
= 2(2y) + 2(1) + 2(y) Using Distributive Property
= 4y + 2 + 2y Multiply
= 4y + 2y + 2 Group Like Terms
= 6y + 2 Combine Like Terms
Result
6y + 2
Page 46 Exercise 26 Answer
6y + 2
= \(6\left(2 \frac{1}{2}\right)+2\) Substitute y = \(2 \frac{1}{2}\)
= 6 . \(\frac{5}{2}\) + 2 Multiply
= 15 + 2 Simplify
= 17 Add
Result
The perimeter of the rectangle is 17 units
Page 46 Exercise 27 Answer
\(\frac{1}{2}\)(2x + 7) Given
= \(\frac{1}{2}(2 x)+\frac{1}{2}(7)\) Using Distributive Property
= \(\frac{2x}{2}\) + \(\frac{7}{2}\) Multiply
= x + \(3 \frac{1}{2}\) Simplify
Result
Rodney use Distributive Property to rewrote \(\frac{1}{2}\)(2x + 7) as x + \(3 \frac{1}{2}\)
Page 46 Exercise 28 Answer
n > \(n^2\) Given
= (0.5) > \((0.5)^2\) Substitute n = 0.5
= 0.5 > 0.25 Simplify
Result
n > \(n^2\) is true for 0 < n < 1
Page 46 Exercise 29 Answer
4x − 3x + 2 Given
= (4 – 3)x + 2 Using Distributive Property
= x + 2 Simplify
Result
Yes, Thea is Correct
Page 46 Exercise 30 Answer
\(\frac{a}{3}+\frac{a}{3}+\frac{a}{3}\) Given
= \(\left(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\right) a\) Using Distributive Property
= \(\frac{3}{3} a\) Add
= a Simplify
Result
a
Page 46 Exercise 31 Answer
2x + 7 + 6x − x
= 2x + 6x − x + 7 Group like terms
= (2 + 6)x − x + 7 Using Distributive Property
= 8x − x + 7 Simplify
= (8x − 1)x + 7 Using Distributive Property
= 7x + 7
Result
Equivalent to: 2x + 7 + 6x − x
7 + 7x and 7x + 7
Not Equivalent to: 2x + 7 + 6x − x
2x + 13 and 14x