To solve the equation: 24(34+x)=1,200
, give the reasons for each of the given steps.
What was done to the previous step to get to the current equation?
(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: 816+24x=1,200
Step 2: 816−816+24x=1,200 − 816
Step 3: 24x=384
Step 4: x=16
Step 1: To get from the original equation to this step, the distributive property is used. The number 24 is distributed to both terms inside the parentheses.
Step 2: To simplify the equation, the constant term 816 is subtracted from both sides of the equation. This is done to isolate the variable term 24x on one side.
Step 3: To further simplify the equation, the result of the subtraction on the left side is calculated, resulting in 384.
Step 4: Finally, to solve for x, the variable is divided by its coefficient, 24. This gives the solution x = 16.
Simplify: −4(2x+5)
(1 point)
Responses
(−4+2x)×(−4+5)
open paren negative 4 plus 2 x close paren times open paren negative 4 plus 5 close paren
(−4×2x)+(−4×5)
open paren negative 4 times 2 x close paren plus open paren negative 4 times 5 close paren
(−4÷2x)+(−4÷5)
open paren negative 4 divided by 2 x close paren plus open paren negative 4 divided by 5 close paren
(−4−2x)+(−4−5)
To simplify the expression -4(2x+5), you would distribute the -4 to both terms inside the parentheses.
This can be shown as:
-4 * 2x + -4 * 5
Which simplifies to:
-8x - 20
So the correct response would be:
(−4×2x)+(−4×5)
Put the steps in order for solving the equation: −2(4x+8)+2x = −5x+10
(1 point)
Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.
Step 1: Distribute -2 to both terms inside the parentheses: -8x - 16 + 2x = -5x + 10.
Step 2: Combine like terms on both sides of the equation: -8x + 2x - 16 = -5x + 10.
Step 3: Simplify the left side of the equation by combining like terms: -6x - 16 = -5x + 10.
Step 4: Move all terms containing x to one side and constant terms to the other side: -6x + 5x = 10 + 16.
Step 5: Combine like terms on both sides of the equation: -x = 26.
Step 6: Multiply both sides of the equation by -1 to solve for x: x = -26.
A student solves the following problem: 2(x - 2) + 5x = 24
Step 1: 2x - 4 + 5x = 24
Step 2: 10x - 4 = 24
Step 3: 10x - 4 + 4 = 24 + 4
Step 4: 10x = 28
Step 5: 10x/10=28/10
Step 6: x = 2.8
Where is the mistake? What did the student do incorrectly?
(1 point)
Responses
Step 5: The student should have multiplied by 10 on both sides, not divided by 10.
Step 5: The student should have multiplied by 10 on both sides, not divided by 10.
Step 3: The student should have subtracted 4 from both sides, not added 4.
Step 3: The student should have subtracted 4 from both sides, not added 4.
Step 1: The student should have only distributed the 2 and x, not the x & -2.
Step 1: The student should have only distributed the 2 and x, not the x & -2.
Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.
The mistake the student made is in Step 2. Instead of adding 2x and 5x to get 7x, they incorrectly multiplied 2x and 5 to get 10x.
So the correct response would be: Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.