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FLUENCY AND SKILLS PRACTICE
Name:
LESSON 15
Expanding Expressions

Expand each expression. Combine like terms where possible.

14(x-2)

2-3(x+7)

3-4(-x-8)

4(1)/(3)(x-9)

5-(1)/(4)(x+16)

6-(1)/(5)(-x-35)

7(2)/(3)(x+18-2x)

8(3)/(4)(16 x-27-1)

9-12((5)/(6)x-5)+2x

qquad

qquad

qquad

Determine which expressions, if any, are equivalent. Show your work.
104(x-3)

6x-2(x-3)quad x+3(x-2)-6
caminulum Asactates LiC copying permetted for dossioon use.
GRADE 7 + Lesson is
Page 1 ot 2

FLUENCY AND SKILLS PRACTICE $\newline$ Name: $\newline$ LESSON $15$ $\newline$ Expanding Expressions $\newline$ - Expand each expression. Combine like terms where possible. $\newline$ $14(x-2)$ $\newline$ $2-3(x+7)$ $\newline$ $3-4(-x-8)$ $\newline$ $4 \frac{1}{3}(x-9)$ $\newline$ $5-\frac{1}{4}(x+16)$ $\newline$ $6-\frac{1}{5}(-x-35)$ $\newline$ $7 \frac{2}{3}(x+18-2 x)$ $\newline$ $8 \frac{3}{4}(16 x-27-1)$ $\newline$ $9-12\left(\frac{5}{6} x-5\right)+2 x$ $\newline$ $\qquad$ $\newline$ $\qquad$ $\newline$ $\qquad$ $\newline$ > Determine which expressions, if any, are equivalent. Show your work. $2-3(x+7)$ $2$ $\newline$ $6 x-2(x-3) \quad x+3(x-2)-6$ $\newline$ caminulum Asactates LiC copying permetted for dossioon use. $\newline$ GRADE $7$ + Lesson is $\newline$ Page $1$ ot $2$

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Sine and cosine of complementary angles

Full solution

Q. FLUENCY AND SKILLS PRACTICE

\newline

Name:

\newline

LESSON

15

\newline

Expanding Expressions

\newline

- Expand each expression. Combine like terms where possible.

\newline

14(x-2)

\newline

2-3(x+7)

\newline

3-4(-x-8)

\newline

4 \frac{1}{3}(x-9)

\newline

5-\frac{1}{4}(x+16)

\newline

6-\frac{1}{5}(-x-35)

\newline

7 \frac{2}{3}(x+18-2 x)

\newline

8 \frac{3}{4}(16 x-27-1)

\newline

9-12\left(\frac{5}{6} x-5\right)+2 x

\newline

\qquad

\newline

\qquad

\newline

\qquad

\newline

> Determine which expressions, if any, are equivalent. Show your work.

2-3(x+7)

2

\newline

6 x-2(x-3) \quad x+3(x-2)-6

\newline

caminulum Asactates LiC copying permetted for dossioon use.

\newline

GRADE

7

+ Lesson is

\newline

Page

1

ot

2

Distribute $14$ into $(x-2)$ : Distribute $14$ into $(x-2)$ . $\newline$ Calculation: $14 \times x - 14 \times 2 = 14x - 28$ .
Distribute $-3$ into $(x+7)$ : Distribute $-3$ into $(x+7)$ . $\newline$ Calculation: $-3 \times x - 3 \times 7 = -3x - 21$ .
Distribute $-4$ into $(-x-8)$ : Distribute $-4$ into $(-x-8)$ . $\newline$ Calculation: $-4 \times -x - 4 \times -8 = 4x + 32$ .
Distribute $\frac{4}{3}$ into $(x-9)$ : Distribute $\frac{4}{3}$ into $(x-9)$ . $\newline$ Calculation: \left(\frac{\(4\)}{\(3\)}\right) \times x - \left(\frac{\(4\)}{\(3\)}\right) \times \(9 = \left(\frac{ $4$ }{ $3$ }\right)x - $12$ .
Distribute $-\frac{1}{4}$ into $(x+16)$ : Distribute $-\frac{1}{4}$ into $(x+16)$ . $\newline$ Calculation: -\left(\frac{\(1\)}{\(4\)}\right) * x - \left(\frac{\(1\)}{\(4\)}\right) * \(16 = -\left(\frac{ $1$ }{ $4$ }\right)x - $4$ .
Distribute $-\frac{1}{5}$ into $(-x-35)$ : Distribute $-\frac{1}{5}$ into $(-x-35)$ . $\newline$ Calculation: -\left(\frac{\(1\)}{\(5\)}\right) * -x - \left(\frac{\(1\)}{\(5\)}\right) * \(-35 = \left(\frac{ $1$ }{ $5$ }\right)x + $7$ .
Distribute $\frac{7}{3}$ into $(x+18-2x)$ : Distribute $\frac{7}{3}$ into $(x+18-2x)$ . $\newline$ Calculation: \left(\frac{7}{3}\right) \cdot x + \left(\frac{7}{3}\right) \cdot 18 - \left(\frac{7}{3}\right) \cdot 2x = \left(\frac{7}{3}\right)x + 42 - \left(\frac{14}{3}\right)x.\(\newlineCombine like terms: \$\left(\frac{7}{3}\right)x - \left(\frac{14}{3}\right)x = -\left(\frac{7}{3}\right)x.\(\newline\)Final expression: \$-\left(\frac{7}{3}\right)x + 42\).
Distribute \(\frac{3}{4}\) into \((16x-27-1)\): Distribute \(\frac{3}{4}\) into \((16x-27-1)\).\(\newline\)Calculation: \(\left(\frac{3}{4}\right) \times 16x - \left(\frac{3}{4}\right) \times 27 - \left(\frac{3}{4}\right) \times 1 = 12x - \left(\frac{81}{4}\right) - \left(\frac{3}{4}\right)\).\(\newline\)Combine like terms: \(- \left(\frac{81}{4}\right) - \left(\frac{3}{4}\right) = - \left(\frac{84}{4}\right) = -21\).\(\newline\)Final expression: \(12x - 21\).
Distribute \(-12\) into \(\left(\frac{5}{6}x-5\right)\) and add \(2x\): Distribute \(-12\) into \(\left(\frac{5}{6}x-5\right)\) and add \(2x\).\(\newline\)Calculation: \(-12 \times \left(\frac{5}{6}\right)x + 12 \times 5 + 2x = -10x + 60 + 2x.\(\newline\)Combine like terms: \$-10x + 2x = -8x.\(\newline\)Final expression: \$-8x + 60.\)
Distribute \(104\) into \((x-3)\): Distribute \(104\) into \((x-3)\).\(\newline\)Calculation: \(104 \times x - 104 \times 3 = 104x - 312\).
Distribute \(6x\) into \(-2(x-3)\) and combine with \(x+3(x-2)-6\): Distribute \(6x\) into \(-2(x-3)\) and combine with \(x+3(x-2)-6\).\(\newline\)Calculation: \(6x - 2 \times x + 2 \times 3 + x + 3 \times x - 3 \times 2 - 6\).\(\newline\)Combine like terms: \(6x - 2x + x + 3x = 8x\).\(\newline\)Final expression: \(8x + 6 - 6\).

More problems from Sine and cosine of complementary angles

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Which is equal to

\sin 75^\circ

\newline

\newline

\cos 25^\circ

\newline

\cos 15^\circ

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\newline

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Posted 26 days ago

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28+56 t+28 w

to identify the equivalent expressions.

\newline

2

\newline

2(56+112 t+56 w)

\newline

28(1+2 t+w)

\newline

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\newline

7(4+8 t+4 w)

Posted 2 months ago

Question

In an election between two candidates Joseph and Judith,

60\%

of the total number of voters did not vote for Joseph and

50\%

of the total number of voters did not vote for Judith. If it is known that each voter can vote for only one candidate, what percentage of voters did not cast their votes? [With calculator]

\newline

5

\newline

10

\newline

20

\newline

30

Posted 2 months ago

Question

Jack, Tom, Beth, and Ruth each have a number of marbles. Jack has

10

marbles, the least, while Tom has

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marbles, the highest. Which of the following could be the average of the number of marbles present with all of them, given that no two of them has the same number of marbles?

\newline

A)\ \$13

\newline

B)\ \$17

\newline

C)\ \$23

\newline

D)\ \$26

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\newline

1-6 y+5+6 x-5 x+4

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Click and drag like terms onto each other to simplify fully.

\newline

-1-4 y^{3}-2 x^{3}+5 x+2-7-x^{3}

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Solve the system:

\newline

\begin{array}{c} x+6 y=17 \\ -x+3 y=-8 \end{array}

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Solve the sinstem:

\newline

\begin{cases} x+6y=17 \ -x+3y=-8 \end{cases}

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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

\newline

7,-35,175, \ldots

\newline

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\newline

-42

\newline

-\frac{1}{5}

\newline

42

Posted 2 months ago

Question

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

\newline

4 x-1, \quad 3 x-1, \quad 2 x-1, \quad \text {.. }

\newline

1

\newline

-x

\newline

x

\newline

-1

Posted 2 months ago