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Math  /  Algebra

QuestionSelect the expressions that are equivalent to −4(9t+6)+8-4(9 t+6)+8. (9t+6)⋅−4+8−4(6+5t+4t)+8−36t−16−4(6t+9)+8\begin{array}{c} (9 t+6) \cdot-4+8 \\ -4(6+5 t+4 t)+8 \\ -36 t-16 \\ -4(6 t+9)+8 \end{array}

Studdy Solution

STEP 1

1. We need to simplify the expression −4(9t+6)+8-4(9t + 6) + 8.
2. We will compare the simplified expression to each given option to determine equivalence.

STEP 2

1. Simplify the expression −4(9t+6)+8-4(9t + 6) + 8.
2. Compare the simplified expression to each given option.
3. Determine which expressions are equivalent.

STEP 3

Simplify the expression −4(9t+6)+8-4(9t + 6) + 8:
First, distribute −4-4 to both terms inside the parentheses:
−4×9t=−36t -4 \times 9t = -36t −4×6=−24 -4 \times 6 = -24
So, −4(9t+6)-4(9t + 6) becomes:
−36t−24 -36t - 24
Now, add 8 to the expression:
−36t−24+8 -36t - 24 + 8
Combine the constant terms:
−36t−16 -36t - 16
The simplified expression is:
−36t−16 -36t - 16

STEP 4

Compare the simplified expression −36t−16-36t - 16 to each given option:
1. (9t+6)⋅−4+8(9t + 6) \cdot -4 + 8:
Distribute −4-4:
−4×9t=−36t -4 \times 9t = -36t −4×6=−24 -4 \times 6 = -24
Add 8:
−36t−24+8=−36t−16 -36t - 24 + 8 = -36t - 16
This is equivalent.
2. −4(6+5t+4t)+8-4(6 + 5t + 4t) + 8:
Combine like terms inside the parentheses:
5t+4t=9t 5t + 4t = 9t
The expression becomes −4(6+9t)+8-4(6 + 9t) + 8, which simplifies to:
−36t−24+8=−36t−16 -36t - 24 + 8 = -36t - 16
This is equivalent.
3. −36t−16-36t - 16:
This matches the simplified expression exactly.
This is equivalent.
4. −4(6t+9)+8-4(6t + 9) + 8:
Distribute −4-4:
−4×6t=−24t -4 \times 6t = -24t −4×9=−36 -4 \times 9 = -36
Add 8:
−24t−36+8=−24t−28 -24t - 36 + 8 = -24t - 28
This is not equivalent.

STEP 5

The expressions that are equivalent to −4(9t+6)+8-4(9t + 6) + 8 are:
1. (9t+6)⋅−4+8(9t + 6) \cdot -4 + 8
2. −4(6+5t+4t)+8-4(6 + 5t + 4t) + 8
3. −36t−16-36t - 16

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