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)
The first step is to distribute the 24 to both terms inside the parentheses. This is done to simplify the expression by removing the parentheses and performing the multiplication.
The equation after distributing is: 816 + 24x = 1,200.
Next, we subtract 816 from both sides of the equation. This is done to isolate the term with the variable (24x) on one side of the equation.
The equation after subtracting 816 is: 24x = 384.
Finally, we divide both sides of the equation by 24 to solve for x. This is done to isolate the variable x and find its value.
The final equation after dividing by 24 is: x = 16.
Therefore, the previous step was dividing both sides of the equation by 24 to get to the current equation.
−4(2x+5) (1 point) Responses (−4−2x)+(−4−5) open paren negative 4 minus 2 x close paren plus open
To solve the equation -4(2x+5), the first step is to distribute -4 to both terms inside the parentheses. This is done to simplify the expression by removing the parentheses and performing the multiplication.
-4(2x+5) becomes -8x - 20 after distributing.
Therefore, the previous step was distributing -4 to both terms inside the parentheses to get to the current equation.
Simplify: −4(2x+5)
(1 point)
Responses
(−4−2x)+(−4−5)
open paren negative 4 minus 2 x close paren plus open paren negative 4 minus 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)
open paren negative 4 plus 2 x close paren times open paren negative 4 plus 5 close paren
(−4×2x)+(−4×5)
To simplify -4(2x+5), the first step is to distribute -4 to both terms inside the parentheses. This is done by multiplying -4 by each term inside the parentheses.
-4 multiplied by 2x gives -8x, and -4 multiplied by 5 gives -20.
Therefore, the simplified expression is -8x - 20.
The previous step was multiplying -4 by 2x and 5 to get -8x and -20, respectively.
Simplify: −4(2x+5)
(1 point)
Responses
A.(−4−2x)+(−4−5)
B. (−4÷2x)+(−4÷5)
C.(−4+2x)×(−4+5)
D. (−4×2x)+(−4×5)
To simplify -4(2x+5), we need to distribute -4 to both terms inside the parentheses.
This gives us: -4 * 2x + (-4) * 5
Simplifying further, -4 * 2x is -8x, and -4 * 5 is -20.
Therefore, the simplified expression is -8x - 20.
The correct response is D. (−4×2x)+(−4×5)
Put the steps in order for solving the equation: −2(4x+8)+2x = −5x+10
(1 point)
The correct order of steps for solving the equation −2(4x+8)+2x = −5x+10 is:
1. Distribute -2 to both terms inside the parentheses:
This gives us -8x - 16 + 2x = -5x + 10.
2. Combine like terms on both sides of the equation:
-8x + 2x - 16 = -5x + 10
3. Simplify the expression on the left side:
-6x - 16 = -5x + 10
4. Add 5x to both sides of the equation:
-6x - 16 + 5x = -5x + 5x + 10
5. Combine like terms on both sides:
-x - 16 = 10
6. Add 16 to both sides:
-x - 16 + 16 = 10 + 16
7. Simplify the expression on the left side:
-x = 26
8. Multiply both sides by -1:
(-1)(-x) = (-1)(26)
9. Simplify the expression on both sides:
x = -26.
Therefore, the steps in order for solving the equation −2(4x+8)+2x = −5x+10 are:
1. Distribute -2 to both terms inside the parentheses.
2. Combine like terms on both sides of the equation.
3. Simplify the expression on the left side.
4. Add 5x to both sides of the equation.
5. Combine like terms on both sides.
6. Add 16 to both sides.
7. Simplify the expression on the left side.
8. Multiply both sides by -1.
9. Simplify the expression on both sides.
The solution is 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?