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5.

a. Factor to write an equivalent expression:
[tex]\[ -9x + 15y \][/tex]

b. Expand to write an equivalent expression:
[tex]\[ -5(7m - 2) \][/tex]

6.

Priya is simplifying the expression [tex]\(-2(4 - 2x) - 3 - 2x\)[/tex]. Here is her work:
[tex]\[
\begin{align*}
-2(4 - 2x) - 3 - 2x \\
-8 - 2x - 3 - 2x \\
-11 - 4x
\end{align*}
\][/tex]

a. Priya's work is incorrect. Explain the error she made.

b. Write an expression equivalent to [tex]\(-4(x + 3) - 12x + 5\)[/tex] that only has two terms. Simplify.

Sagot :

GinnyAnsweridn
Certainly! Let’s work through each of the parts step-by-step.
### 5. a. Factor to write an equivalent expression:
[tex]\[ -9x + 15y \][/tex]

1. Identify the greatest common factor (GCF) of the coefficients -9 and 15, which is 3.
2. Factor out -3 from both terms:

[tex]\[ -9x + 15y = -3(3x - 5y) \][/tex]

So, the factored expression is:

[tex]\[ -3(3x - 5y) \][/tex]

### 5. b. Expand to write an equivalent expression:
[tex]\[ -5(7m - 2) \][/tex]

1. Apply the distributive property by multiplying -5 with each term inside the parentheses:

[tex]\[ -5 \cdot 7m + (-5) \cdot (-2) = -35m + 10 \][/tex]

So, the expanded expression is:

[tex]\[ -35m + 10 \][/tex]

### 6. a. Priya's work is incorrect. Explain the error she made.
Priya's work:

[tex]\[ \begin{array}{c} -2(4 - 2x) - 3 - 2x \\ -8 - 2x - 3 - 2x \\ -11 - 4x \end{array} \][/tex]

Priya incorrectly distributed the -2 to both terms in the parentheses but made an error with the sign for the second term. The correct steps are:
1. Distribute -2 to both terms:

[tex]\[ -2(4 - 2x) = -8 + 4x \][/tex]

Note that [tex]\(-2 \cdot -2x\)[/tex] should be [tex]\(+4x\)[/tex], not [tex]\(-2x\)[/tex] as Priya wrote.

2. Combine all terms:

[tex]\[ -8 + 4x - 3 - 2x \][/tex]

Combine the like terms:

[tex]\[ -8 - 3 + 4x - 2x = -11 + 2x \][/tex]

So, Priya's corrected expression is:

[tex]\[ -11 + 2x \][/tex]

### 6. b. Write an expression equivalent to [tex]\( -4(x + 3) - 12x + 5 \)[/tex] that only has two terms. Simplify.
1. Distribute -4 across the terms in the parentheses:

[tex]\[ -4(x + 3) = -4x - 12 \][/tex]

2. Combine all terms in the expression:

[tex]\[ -4x - 12 - 12x + 5 \][/tex]

3. Combine the like terms:

[tex]\[ -4x - 12x - 12 + 5 = -16x - 7 \][/tex]

So, the simplified expression is:

[tex]\[ -16x - 7 \][/tex]
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