Question

1. $3x = 15$
2. $9y - 9$

$9(y - 1)$

1. $35 - 28$

$7(5 - 4)$

1. $4x + 22$
2. $20a + 144$

$4(5a + 36)$

1. $7w - 63v$
2. $12 - 2k$

$2(6 - k)$

1. $40 + 16m$
2. $30 - 54u$

$6(5 - 9u)$

1. $12p + 18q$
2. $28a - 60b + 20$

$4(7a - 15b + 5)$
directions: translate each expression, then write the expression in factored form.

1. “the sum of four times a number and twenty - four”

$4x + 24$

1. “the difference between nine times a number and seventy - two”
2. “ten times a number, subtracted from eighteen”
3. “thirty more than the product of six and a number”

directions: write three expressions that are equivalent to the given expression.

1. $7a + 21$

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1. $24x + 20y$

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Explanation:

Problem 20: \( 7a + 21 \) - Writing Equivalent Expressions

Step 1: Factor out 7

We can factor out the greatest common factor (GCF) of \( 7a \) and \( 21 \), which is 7.
\( 7a + 21 = 7(a + 3) \)

Step 2: Distribute a different factor (e.g., 14)

We can also multiply the factored form by a constant and then distribute. Let's multiply by 2:
\( 2 \times 7(a + 3) = 14(a + 3) = 14a + 42 \)

Step 3: Rearrange terms (though not necessary, but to show equivalence)

We can also write it as \( 21 + 7a \) (addition is commutative)

Problem 21: \( 24x + 20y \) - Writing Equivalent Expressions

Step 1: Factor out the GCF (4)

The GCF of \( 24x \) and \( 20y \) is 4.
\( 24x + 20y = 4(6x + 5y) \)

Step 2: Factor out a different common factor (e.g., 2)

\( 2(12x + 10y) = 24x + 20y \) (after distributing)

Step 3: Multiply the factored form by a constant (e.g., 3)

\( 3 \times 4(6x + 5y) = 12(6x + 5y) = 72x + 60y \)

Final Answers for Equivalent Expressions:

Problem 20 (\( 7a + 21 \)):

1. \( 7(a + 3) \)
2. \( 14a + 42 \)
3. \( 21 + 7a \)

Problem 21 (\( 24x + 20y \)):

1. \( 4(6x + 5y) \)
2. \( 2(12x + 10y) \)
3. \( 72x + 60y \)

Answer:

Step 1: Factor out the GCF (4)

The GCF of \( 24x \) and \( 20y \) is 4.
\( 24x + 20y = 4(6x + 5y) \)

Step 2: Factor out a different common factor (e.g., 2)

\( 2(12x + 10y) = 24x + 20y \) (after distributing)

Step 3: Multiply the factored form by a constant (e.g., 3)

\( 3 \times 4(6x + 5y) = 12(6x + 5y) = 72x + 60y \)

Final Answers for Equivalent Expressions:

Problem 20 (\( 7a + 21 \)):

1. \( 7(a + 3) \)
2. \( 14a + 42 \)
3. \( 21 + 7a \)

Problem 21 (\( 24x + 20y \)):

1. \( 4(6x + 5y) \)
2. \( 2(12x + 10y) \)
3. \( 72x + 60y \)