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Question

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 1

To determine which responses are equivalent to the expression $(3x-8)+(2x+5)-(4x-8)$, we will simplify the original expression step by step:

1. Start with the original expression: $$(3x-8)+(2x+5)-(4x-8)$$

2. Distribute the negative sign in front of $-(4x-8)$: $$(3x-8)+(2x+5)-4x+8$$

3. Combine the terms:

   • Combine the $x$ terms: $3x+2x-4x=(3+2-4)x=x$
   • Combine the constant terms: $-8+5+8=(-8+5+8)=5$

4. The simplified expression is: $$x+5$$

Now, let's check each response to see if it simplifies to $x+5$:

1. Response: $3x-8+2x+5-4x-8$

   • Combine: $3x+2x-4x-8-8+5=(3+2-4)x+(-8-8+5)=x-11$ (Not equivalent)

2. Response: $3x-8+2x+5-4x+8$

   • Combine: $3x+2x-4x-8+8+5=(3+2-4)x+(0+5)=x+5$ (Equivalent)

3. Response: $3x+2x-4x-8+5+8$

   • Combine: $3x+2x-4x-8+5+8=(3+2-4)x+(0+5)=x+5$ (Equivalent)

4. Response: $5x-4x-8+5+8$

   • Combine: $5x-4x-8+5+8=(5-4)x+(0+5)=x+5$ (Equivalent)

5. Response: $x-8+5+8$

   • Combine: $x-8+5+8=x+(5-8+8)=x+5$ (Equivalent)

6. Response: $x-13+8$

   • Combine: $x-13+8=x-5$ (Not equivalent)

7. Response: $x-3+8$

   • Combine: $x-3+8=x+5$ (Equivalent)

8. Response: $x-21$

   • Not equivalent (It's just $x-21$).

9. Response: $x+5$

   • This is obviously equivalent.

Thus, the expressions that are equivalent to $(3x-8)+(2x+5)-(4x-8)$ are:

• $3x-8+2x+5-4x+8$
• $3x+2x-4x-8+5+8$
• $5x-4x-8+5+8$
• $x-8+5+8$
• $x-3+8$
• $x+5$

So the selected responses are:

• $3x-8+2x+5-4x+8$
• $3x+2x-4x-8+5+8$
• $5x-4x-8+5+8$
• $x-8+5+8$
• $x-3+8$
• $x+5$

Answer 2

10 of 2710 of 27 Items

Question
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 3

To determine which expressions are equivalent to $5(3x+9)$, we will simplify the original expression step by step:

1. Start with the original expression: $$5(3x+9)$$

2. Apply the distributive property: $$5\times 3x+5\times 9=15x+45$$

The simplified expression is: $$15x+45$$

Now let's check each response to see if it is equivalent to $15x+45$:

1. Response: $8x+14$

   • This does not match. (Not equivalent)

2. Response: $5\times 3x+5\times 9$

   • This simplifies to $15x+45$ (Equivalent).

3. Response: $5\times 3x+9$

   • This simplifies to $15x+9$ (Not equivalent).

4. Response: $15x+9$

   • This does not match. (Not equivalent)

5. Response: $15x+45$

   • This matches exactly. (Equivalent).

Thus, the expressions that are equivalent to $5(3x+9)$ are:

• $5\times 3x+5\times 9$
• $15x+45$

In summary, the correct responses are:

• $5\times 3x+5\times 9$
• $15x+45$

Answer 4

11 of 2711 of 27 Items

Question
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
2.9
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Answer 5

To simplify the expression $-4.08÷1.2-(-4.2)\times 1.5$, we will carry out the calculations step by step.

1. Calculate $-4.08÷1.2$: $$-4.08÷1.2=-3.4$$

2. Calculate $-(-4.2)\times 1.5$:

   • First, calculate $-4.2\times 1.5$: $$-4.2\times 1.5=-6.3$$
   • Since we have a negative of a negative: $$-(-4.2\times 1.5)=6.3$$

3. Now combine the results: $$-3.4+6.3=2.9$$

So, the simplified expression results in $2.9$.

Among the given responses, the correct answer is:

• 2.9

Answer 6

12 of 2712 of 27 Items

Question
Solve the equation for y.

5y−10=−25


(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Step 1:
Step 2:
Solution:
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Answer 7

To solve the equation $5y-10=-25$ for $y$, we can follow these steps:

Step 1: Isolate the term with $y$

Add $10$ to both sides of the equation to eliminate the $-10$:

$$5y-10+10=-25+10$$

This simplifies to:

$$5y=-15$$

Step 2: Solve for $y$

Now, divide both sides by $5$:

$$y=\frac{-15}{5}$$

This simplifies to:

$$y=-3$$

Solution:

So, the solution is:

$$y=-3$$

Make sure to enter the solution correctly in your input fields.

Answer 8

13 of 2713 of 27 Items

Question
Solve the equation for x.

−3x+4=−8


(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Step 1:
Step 2:
Solution:
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Answer 9

To solve the equation $-3x+4=-8$ for $x$, we can follow these steps:

Step 1: Isolate the term with $x$

Subtract $4$ from both sides of the equation to eliminate the $+4$:

$$-3x+4-4=-8-4$$

This simplifies to:

$$-3x=-12$$

Step 2: Solve for $x$

Now, divide both sides by $-3$:

$$x=\frac{-12}{-3}$$

This simplifies to:

$$x=4$$

Solution:

So, the solution is:

$$x=4$$

Make sure to enter the solution correctly in your input fields.

Answer 10

14 of 2714 of 27 Items

Question
The equation −3x−9=−21
is solved as follows. Enter the correct numbers to complete the solution.(1 point)
−3x−9=−21

−3x=

Add 9 to both sides of the equation.

x=
Divide both sides of the equation by -3. If the answer is an improper fraction, enter the improper fraction.

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Answer 11

To solve the equation $-3x-9=-21$, we can follow these steps and fill in the blanks accordingly.

Step-by-step solution:

1. Start with the original equation: $$-3x-9=-21$$

2. Step 1: Add $9$ to both sides of the equation: $$-3x=-21+9$$ So, $$-3x=-12$$

3. Step 2: Now, divide both sides of the equation by $-3$: $$x=\frac{-12}{-3}$$ This simplifies to: $$x=4$$

Summary of answers to fill in:

• After adding $9$ to both sides:
  $-3x=-12$

• After dividing both sides by $-3$:
  $x=4$

So your entries should be:

• For the first blank: -12
• For the second blank: 4