Select all expressions that are equivalent to this algebraic expression.

Question

(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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Answer 1

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 2

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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Answer 3

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 4

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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Answer 5

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 6

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 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.