Question Find all values of $a_0$ that satisfy the equation $|2a-15| = 7$ .

Studdy Solution

STEP 1

Assumptions
1. We are solving for all values of $a$ such that $|2a - 15| = 7$ .
2. We will use the property that $|x| = k$ implies $x = k$ or $x = -k$ for any real number $k$ .

STEP 2

The absolute value equation $|2a - 15| = 7$ can be split into two separate equations based on the definition of absolute value:
1. $2a - 15 = 7$
2. $2a - 15 = -7$

STEP 3

First, we solve the equation $2a - 15 = 7$ .
Add 15 to both sides of the equation to isolate the term with $a$ on one side:
$2a - 15 + 15 = 7 + 15$

STEP 4

Simplify the equation:
$2a = 22$

STEP 5

Divide both sides by 2 to solve for $a$ :
$\frac{2a}{2} = \frac{22}{2}$

STEP 6

Simplify the equation to find the first value of $a$ :
$a = 11$

STEP 7

Now, we solve the second equation $2a - 15 = -7$ .
Add 15 to both sides of the equation:
$2a - 15 + 15 = -7 + 15$

STEP 8

Simplify the equation:
$2a = 8$

STEP 9

Divide both sides by 2 to solve for $a$ :
$\frac{2a}{2} = \frac{8}{2}$

STEP 10

Simplify the equation to find the second value of $a$ :
$a = 4$

STEP 11

Combine the two values of $a$ to present the solution:
The values of $a$ that satisfy the equation $|2a - 15| = 7$ are $a = 11$ and $a = 4$ .

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