When solving the equation −12(x+10)=−3, identify the operation that should be done first.(1 point)
Responses
subtract 10
subtract 10
multiply by −2
multiply by negative 2
divide by −2
divide by negative 2
add 10
To solve the equation −12(x+10)=−3, the first operation that should be done is to divide by −12.
Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 less than the cost of an adult ticket. Identify the first step if solving this problem arithmetically, which would find the cost of one adult and one child ticket. (1 point)
Responses
Subtract 6 from 75.
Subtract 6 from 75.
Divide 75 by 6.
Divide 75 by 6.
Divide 75 by 3.
Divide 75 by 3.
Add 3 to 75.
The first step to find the cost of one adult and one child ticket in this problem would be to divide 75 by 6.
To solve the equation −12(x+10)=−3, the first operation that should be done is to simplify the expression inside the parentheses, which is (x+10). This is because the equation uses the distributive property of multiplication over addition/subtraction.
To simplify (x+10), you need to distribute the -12 to both terms inside the parentheses. This means multiplying -12 by x and -12 by 10. The expression becomes -12x - 120.
Now the equation becomes -12x - 120 = -3.
To solve for x, you need to isolate the variable x. In this case, you can start by getting rid of the constant term -120 by adding 120 to both sides of the equation.
-12x - 120 + 120 = -3 + 120
This simplifies to -12x = 117.
Now, to solve for x, you need to divide both sides of the equation by the coefficient of x, which is -12.
-12x / -12 = 117 / -12
This gives you x = -9.75.
Therefore, the operation that should be done first in solving the equation −12(x+10)=−3 is to distribute the -12 to the terms inside the parentheses.