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Select the action you would use to solve [tex]\frac{x}{4} = 16[/tex]. Then select the property that justifies that action.

A. Action: Add 4 to both sides.
B. Property: Division property of equality.
C. Action: Multiply both sides by 4.
D. Property: Multiplication property of equality.
E. Action: Divide both sides by 4.
F. Property: Addition property of equality.

Sagot :

GinnyAnswer
To solve the equation [tex]\(\frac{x}{4} = 16\)[/tex], you need to isolate the variable [tex]\(x\)[/tex].

First, let's identify what action we should use:

1. The equation is given as [tex]\(\frac{x}{4} = 16\)[/tex].
2. To isolate [tex]\(x\)[/tex], we need to eliminate the fraction.
3. The fraction [tex]\(\frac{x}{4}\)[/tex] indicates that [tex]\(x\)[/tex] is divided by 4.
4. To undo this division, we need to perform the opposite operation, which is multiplication.

Therefore, the action to use is to multiply both sides by 4.

So the correct action is:
C. Action: Multiply both sides by 4.

Next, let's identify the property that justifies this action:

1. The property that allows us to multiply both sides of an equation by the same number is called the Multiplication Property of Equality.
2. This property states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal.

Therefore, the property that justifies the action is:
D. Property: Multiplication property of equality.

Putting it all together, the correct choices are:

C. Action: Multiply both sides by 4.
D. Property: Multiplication property of equality.
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