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Math

Question Find a number xx such that 48−x=4x−748 - x = 4x - 7.

Studdy Solution

STEP 1

Assumptions
1. We are looking for a number, which we will denote as x x .
2. The phrase "forty-eight decreased by a number" translates to 48−x 48 - x .
3. The phrase "the same as" indicates equality.
4. The phrase "the difference of four times a number and seven" translates to 4x−7 4x - 7 .
5. We need to set up an equation that equates the two expressions from steps 2 and 4.

STEP 2

Translate the sentence "Forty-eight decreased by a number is the same as the difference of four times a number and seven" into a mathematical equation.
48−x=4x−748 - x = 4x - 7

STEP 3

Add x x to both sides of the equation to bring all the x x terms to one side.
48−x+x=4x−7+x48 - x + x = 4x - 7 + x

STEP 4

Simplify both sides of the equation.
48=5x−748 = 5x - 7

STEP 5

Add 7 to both sides of the equation to isolate the term with x x on one side.
48+7=5x−7+748 + 7 = 5x - 7 + 7

STEP 6

Simplify both sides of the equation.
55=5x55 = 5x

STEP 7

Divide both sides of the equation by 5 to solve for x x .
555=5x5\frac{55}{5} = \frac{5x}{5}

STEP 8

Simplify both sides of the equation to find the value of x x .
11=x11 = x
The number we were looking for is 11.

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