Question

Select all expressions that are equivalent to this algebraic expression.

(2x−1)−3.25(x+3)
(1 point)
Responses

2x−1−3.25x−9.75
2 x minus 1 minus 3 point 2 5 x minus 9 point 7 5

2x−3.25x−1−9.75
2 x minus 3 point 2 5 x minus 1 minus 9 point 7 5

−1.25x−1−9.75
negative 1 point 2 5 x minus 1 minus 9 point 7 5

−1.25x−10.75
negative 1 point 2 5 x minus 10 point 7 5

2x−1−3.25x+9.75
2 x minus 1 minus 3 point 2 5 x plus 9 point 7 5

1.25x+10.75
1 point 2 5 x plus 10 point 7 5

−1.25x−4
negative 1 point 2 5 x minus 4
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page 4 of 4

Answer 1

14 of 1614 of 16 Items










































Question
Select all of the expressions that are equivalent to this algebraic expression.

(3x−8)+(2x+5)−(4x−8)
(1 point)
Responses

3x−8+2x+5−4x−8
3 x minus 8 plus 2 x plus 5 minus 4 x minus 8

3x−8+2x+5−4x+8
3 x minus 8 plus 2 x plus 5 minus 4 x plus 8

3x+2x−4x−8+5+8
3 x plus 2 x minus 4 x minus 8 plus 5 plus 8

5x−4x−8+5+8
5 x minus 4 x minus 8 plus 5 plus 8

x−8+5+8
x minus 8 plus 5 plus 8

x−13+8
x minus 13 plus 8

x−3+8
x minus 3 plus 8

x−21
x minus 21

x+5
x plus 5
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page 4 of 4
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Answer 2

Select all expressions that are equivalent to this algebraic expression:

5(3x+9)


(1 point)
Responses

8x+14
8 x plus 14

5×3x+5×9
5 times 3 x plus 5 times 9

5×3x+9
5 times 3 x plus 9

15x+9
15 x plus 9

15x+45
15 x plus 45
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page 4 of 4

Answer 3

Simplify the expression.

−4.08÷1.2−(−4.2)×1.5
(1 point)
Responses

-2.9
-2.9

9.7
9.7

-9.7
-9.7

2.9

Answer 4

To determine which expressions are equivalent to the algebraic expression \((2x−1)−3.25(x+3)\), we first simplify this expression.

1. **Distribute \(-3.25\)** to both terms in \( (x + 3) \):
\[
-3.25(x + 3) = -3.25x - 9.75
\]

2. **Combine with \( (2x - 1) \)**:
\[
(2x - 1) - 3.25(x + 3) = 2x - 1 - 3.25x - 9.75
\]

3. **Combine like terms**:
Combine the \(x\) terms:
\[
2x - 3.25x = -1.25x
\]
Combine the constant terms:
\[
-1 - 9.75 = -10.75
\]

Putting it all together gives us:
\[
-1.25x - 10.75
\]

Now we can compare this result to the options provided:

1. **\(2x - 1 - 3.25x - 9.75\)** → Equivalent.
2. **\(2x - 3.25x - 1 - 9.75\)** → Equivalent.
3. **\(-1.25x - 1 - 9.75\)** → Not equivalent (combines to \(-1.25x - 10.75\), but formatted differently).
4. **\(-1.25x - 10.75\)** → Equivalent.
5. **\(2x - 1 - 3.25x + 9.75\)** → Not equivalent (incorrect sign for the last term).
6. **\(1.25x + 10.75\)** → Not equivalent (entirely different sign for \(x\)).
7. **\(-1.25x - 4\)** → Not equivalent (incorrect constant term).

Therefore, the equivalent expressions are:

- **\(2x - 1 - 3.25x - 9.75\)**
- **\(2x - 3.25x - 1 - 9.75\)**
- **\(-1.25x - 10.75\)**

These three expressions are equivalent to \((2x−1)−3.25(x+3)\).

Answer 5

To find the equivalent expressions for the given algebraic expression \((3x−8)+(2x+5)−(4x−8)\), we can simplify it step-by-step.

### Step 1: Distribute any negative signs
The expression is:
\[
(3x - 8) + (2x + 5) - (4x - 8)
\]
Distributing the negative sign across \(-(4x - 8)\) results in:
\[
(3x - 8) + (2x + 5) - 4x + 8
\]

### Step 2: Combine like terms
Now, let's combine like terms:
1. Combine the \(x\) terms:
\[
3x + 2x - 4x = (3 + 2 - 4)x = 1x = x
\]

2. Combine the constant terms:
\[
-8 + 5 + 8 = (-8 + 8) + 5 = 0 + 5 = 5
\]

### Final Simplified Expression
Putting it all together:
\[
(3x - 8) + (2x + 5) - (4x - 8) = x + 5
\]

### Identifying Equivalent Expressions
Now, let's check through the provided options to see which ones are equivalent to \(x + 5\):

1. **\(3x−8+2x+5−4x−8\)**: Equivalent.
2. **\(3x−8+2x+5−4x+8\)**: Not equivalent (the last term should not be +8).
3. **\(3x+2x−4x−8+5+8\)**: Equivalent (after combining terms gives us \(x + 5\)).
4. **\(5x−4x−8+5+8\)**: Equivalent (after simplifying gives us \(x + 5\)).
5. **\(x−8+5+8\)**: Equivalent (simplifies to \(x + 5\)).
6. **\(x−13+8\)**: Not equivalent (simplifies to \(x - 5\)).
7. **\(x−3+8\)**: Not equivalent (simplifies to \(x + 5\)).
8. **\(x−21\)**: Not equivalent.
9. **\(x+5\)**: Equivalent.

### Conclusion
The equivalent expressions are:
- \(3x−8+2x+5−4x−8\)
- \(3x+2x−4x−8+5+8\)
- \(5x−4x−8+5+8\)
- \(x−8+5+8\)
- \(x+5\)

These are the expressions that simplify to \(x + 5\).

Answer 6

To determine which expressions are equivalent to the algebraic expression \(5(3x + 9)\), we will simplify this expression step by step.

### Step 1: Distribute the 5
Distributing \(5\) across the terms in the parentheses gives us:
\[
5(3x + 9) = 5 \cdot 3x + 5 \cdot 9 = 15x + 45
\]

### Final Result
The simplified expression is:
\[
15x + 45
\]

### Identifying Equivalent Expressions
Now let's compare this result to the options provided:

1. **\(8x + 14\)**: Not equivalent.
2. **\(5 \times 3x + 5 \times 9\)**: Equivalent (this represents the original expression before simplifying).
3. **\(5 \times 3x + 9\)**: Not equivalent (the correct term should be \(45\) instead of \(9\)).
4. **\(15x + 9\)**: Not equivalent (the correct constant term is \(45\)).
5. **\(15x + 45\)**: Equivalent (this matches our final simplified expression).

### Conclusion
The equivalent expressions to \(5(3x + 9)\) are:
- **\(5 \times 3x + 5 \times 9\)**
- **\(15x + 45\)**

These two expressions are equivalent to the original expression.

Answer 7

To simplify the expression \(-4.08 \div 1.2 - (-4.2) \times 1.5\), we'll handle each part step by step.

### Step 1: Simplify \(-4.08 \div 1.2\)

Calculate:
\[
-4.08 \div 1.2 = -3.4
\]

### Step 2: Simplify \(-(-4.2) \times 1.5\)

First, simplify \(-(-4.2)\):
\[
-(-4.2) = 4.2
\]

Now, calculate \(4.2 \times 1.5\):
\[
4.2 \times 1.5 = 6.3
\]

### Step 3: Combine the results

Now, substitute back into the expression:
\[
-3.4 - 6.3
\]

Calculate:
\[
-3.4 - 6.3 = -9.7
\]

### Final Result
The simplified expression is:
\[
\boxed{-9.7}
\]

So the correct response is **-9.7**.