Question

One less than two times a number is equal to 11 more than four times the number

Answer 1

Answer: x= -6

Explanation:

Each word in a word problem translates to a mathematical symbol

> 1 less than => - 1

> two times a number => 2x

put that together 1 less than two times a number means:

2x-1

> is => =

> 11 more => 11+

> four times the number => 4x

put it all together

2x-1=11+4x bring all like terms to each side

-2x = 12 solve for x

x= -6

Answer 2

n = -6

Explanation:

We can allow n to represent the unknown number.

• Two times the number is 2n and 1 less than gives us 2n - 1

• Four times the number is 4n and 11 more than gives us 4n + 11

Now, we can set the two expressions equal to each other to find the number, n:

`2n-1=4n+11\\2n=4n+12\\-2n=12\\n=-6`

Finally, we can check if the number fits the equation and the verbal expression by plugging in -6 for n:

Algebraically:

2(-6) - 1 = 4(-6) + 11

-12 - 1 = -24 + 11

-13 = -13

Verbally:

Two times the number -6 is -12 and 1 less than - 12 is -13

Four times the number -6 is -24 and 11 more than this is -13