21 less than half a number is the same as four times the number. What is that number?

Question

i really need help i cannot figure this out and im horrible at math

Answer 1

Let your number be x

Break your problem in small steps:

"half a number" means 1/2(x)

"21 less than half a number" means 1/2(x)-21

"four times a number" means: 4x

Now let's put them together:

"21 less than half a number is the same as four times the number"

1/2(x)-21=4x

Solve for x

Multiple both side of the equation with 2 so we can eliminate fractions:

1/2(x)•2-21•2=2•4x

x-42=8x

Separate all unknowns (those which contains x) from rest of the numbers

x-8x=42

-7x=42

x=-6

Make sure you check your answer

1/2(x)-21=4x

1/2(-6)-21=4(-6)

-3-21=-24

-24=-24 TRUE

Answer 2

21 less than half a number is the same as four times the number. What is that number?

"Twenty-one is less than half of a number" means "half of a number minus twenty-one" or 0.5x - 21

"Is the same as" means "equals"

"Four times the number" means 4x

So the equation is 0.5x - 21 = 4x

To solve the equation:

Step One: Subtract 0.5x from BOTH sides

Result: -21 = 3.5x

Step Two: Divide 3.5 from BOTH sides

Result: 6 = x

So the number that is "21 less than half a number is the same as four times the number" is 6.