Question"Four times the difference of a number and nine is $-30 . "$

Studdy Solution

STEP 1

1. Let the unknown number be denoted by $x$ .
2. The phrase "the difference of a number and nine" translates to the expression $x - 9$ .
3. The phrase "four times the difference" translates to $4(x - 9)$ .
4. The expression $4(x - 9)$ is equal to $-30$ .

STEP 2

1. Translate the word problem into an algebraic equation.
2. Solve the algebraic equation for $x$ .
3. Verify the solution by substituting back into the original word problem.

STEP 3

Translate the word problem into an algebraic equation.
$4(x - 9) = -30$

STEP 4

Distribute the $4$ on the left-hand side of the equation.
$4x - 36 = -30$

STEP 5

Add $36$ to both sides of the equation to isolate the term with $x$ .
$4x - 36 + 36 = -30 + 36$ $4x = 6$

STEP 6

Divide both sides of the equation by $4$ to solve for $x$ .
$x = \frac{6}{4}$ $x = \frac{3}{2}$

STEP 7

Verify the solution by substituting $x = \frac{3}{2}$ back into the original word problem.

STEP 8

Calculate the difference between the number and nine for $x = \frac{3}{2}$ :
$\frac{3}{2} - 9 = \frac{3}{2} - \frac{18}{2} = -\frac{15}{2}$

STEP 9

Multiply the result by $4$ and check if it equals $-30$ :
$4 \left(-\frac{15}{2}\right) = -30$
Solution: The number is $\frac{3}{2}$ .

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