Question

Negative 48 decreased by a number is the same as the sum of 4 times a number and 7

Answer 1

Translation from words to formulas is the hard part.
First identify the quantities involved.
let x be “the number”

Next write down the equation(s) related to the number.
Translate “48 decreased by a number” into (48 - x)
Translate “is the same as” to “=“
Translate “the difference of 4 times the number and 7” into (4x - 7)

now put them together:
48-x = 4x-7

This is the equation with variables on both sides.

I assume you can take it from here, but for the rest of the students watching...
We want x’s on one side of the equals sign and numbers on the other.

First, to “move” the - x from the left side to the right, ADD x to both sides. Now we have
48 = 4x -7 +x
next collect the x’s
48 = 4x + x - 7
next “move” the - 7 from the right side to the left, by ADDING 7 to both sides.
48 + 7 = 5x
collect the numbers
55 = 5x

finally we want to get to ONE x, rather than 5, so divide both sides by 5.

11 = x

Answer 2

Let the unknown number be x.

Negative 48 decreased by a number: -48 - x

Is the same as the sum of 4 times a number and 7:

-48 - x = 4x + 7

Let's find the number:

-48x - x = 4x + 7

-48x = 4x + 7

Subtract 4x from both sides:

-48x - 4x = 4x - 4x + 7

-52x = 7