Which of the following should be done to both sides of the equation −6x=48 to solve the value of x?(1 point)
Responses
divide by 6
divide by 6
multiply by −6
multiply by negative 6
add 6
add 6
divide by −6
divide by -6
To solve the value of x in the equation −6x = 48, you should divide both sides of the equation by -6.
To solve the equation −6x = 48 and find the value of x, we need to perform the same operation on both sides of the equation. This ensures that we maintain the equality of the equation.
Looking at the given options, we can eliminate "add 6" since adding 6 to both sides of the equation will not help us isolate x.
Next, let's consider "multiply by −6" or "multiply by negative 6." This operation is incorrect because if we multiply both sides of the equation by −6, it will change the sign of both sides, making it −6 × (−6x) = −6 × 48. This would result in a different equation, not equivalent to the original.
Finally, we have "divide by 6" and "divide by −6" as our remaining options. To isolate x, we want to get rid of the coefficient (the number multiplied by x) on the left side of the equation. To do this, we need to divide both sides by the coefficient.
In this case, the correct operation is to "divide by −6." Doing so gives us:
(−6x)/−6 = 48/−6
The −6 on the left side cancels out, leaving us with x = 48/−6.
Therefore, the correct option is to "divide by −6" to solve for the value of x.