Question Solve the absolute value equation $2|a|-1=3$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $2|a| - 1 = 3$ .
2. We need to solve for the variable $a$ .
3. The absolute value function $|x|$ returns the non-negative value of $x$ .

STEP 2

First, we want to isolate the absolute value expression on one side of the equation. We can do this by adding 1 to both sides of the equation.
$2|a| - 1 + 1 = 3 + 1$

STEP 3

Simplify both sides of the equation to get the absolute value expression by itself.
$2|a| = 4$

STEP 4

Now, we will divide both sides of the equation by 2 to solve for the absolute value of $a$ .
$\frac{2|a|}{2} = \frac{4}{2}$

STEP 5

Simplify both sides of the equation.
$|a| = 2$

STEP 6

The absolute value equation $|a| = 2$ has two possible solutions because the absolute value of a number is the distance from zero, and it can be either positive or negative.

STEP 7

The first possible solution is when the value inside the absolute value is positive.
$a = 2$

STEP 8

The second possible solution is when the value inside the absolute value is negative.
$a = -2$
Therefore, the solutions to the equation $2|a| - 1 = 3$ are $a = 2$ and $a = -2$ .

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Question Solve the absolute value equation $2|a|-1=3$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $2|a| - 1 = 3$ .
2. We need to solve for the variable $a$ .
3. The absolute value function $|x|$ returns the non-negative value of $x$ .

STEP 2

First, we want to isolate the absolute value expression on one side of the equation. We can do this by adding 1 to both sides of the equation.
$2|a| - 1 + 1 = 3 + 1$

STEP 3

Simplify both sides of the equation to get the absolute value expression by itself.
$2|a| = 4$

STEP 4

Now, we will divide both sides of the equation by 2 to solve for the absolute value of $a$ .
$\frac{2|a|}{2} = \frac{4}{2}$

STEP 5

Simplify both sides of the equation.
$|a| = 2$

STEP 6

The absolute value equation $|a| = 2$ has two possible solutions because the absolute value of a number is the distance from zero, and it can be either positive or negative.

STEP 7

The first possible solution is when the value inside the absolute value is positive.
$a = 2$

STEP 8

The second possible solution is when the value inside the absolute value is negative.
$a = -2$
Therefore, the solutions to the equation $2|a| - 1 = 3$ are $a = 2$ and $a = -2$ .

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Question Solve the absolute value equation 2∣a∣−1=32|a|-1=32∣a∣−1=3.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 2∣a∣−1=32|a| - 1 = 32∣a∣−1=3.2. We need to solve for the variable aaa.3. The absolute value function ∣x∣|x|∣x∣ returns the non-negative value of xxx.

STEP 2

First, we want to isolate the absolute value expression on one side of the equation. We can do this by adding 1 to both sides of the equation.2∣a∣−1+1=3+12|a| - 1 + 1 = 3 + 12∣a∣−1+1=3+1

STEP 3

Simplify both sides of the equation to get the absolute value expression by itself.2∣a∣=42|a| = 42∣a∣=4

STEP 4

Now, we will divide both sides of the equation by 2 to solve for the absolute value of aaa.2∣a∣2=42\frac{2|a|}{2} = \frac{4}{2}22∣a∣​=24​

STEP 5

Simplify both sides of the equation.∣a∣=2|a| = 2∣a∣=2

STEP 6

The absolute value equation ∣a∣=2|a| = 2∣a∣=2 has two possible solutions because the absolute value of a number is the distance from zero, and it can be either positive or negative.

STEP 7

The first possible solution is when the value inside the absolute value is positive.a=2a = 2a=2

STEP 8

The second possible solution is when the value inside the absolute value is negative.a=−2a = -2a=−2Therefore, the solutions to the equation 2∣a∣−1=32|a| - 1 = 32∣a∣−1=3 are a=2a = 2a=2 and a=−2a = -2a=−2.

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Question Solve the absolute value equation $2|a|-1=3$ .

Assumptions
1. We are given the equation $2|a| - 1 = 3$ .
2. We need to solve for the variable $a$ .
3. The absolute value function $|x|$ returns the non-negative value of $x$ .

First, we want to isolate the absolute value expression on one side of the equation. We can do this by adding 1 to both sides of the equation.
$2|a| - 1 + 1 = 3 + 1$

Simplify both sides of the equation to get the absolute value expression by itself.
$2|a| = 4$

Now, we will divide both sides of the equation by 2 to solve for the absolute value of $a$ .
$\frac{2|a|}{2} = \frac{4}{2}$

Simplify both sides of the equation.
$|a| = 2$

The absolute value equation $|a| = 2$ has two possible solutions because the absolute value of a number is the distance from zero, and it can be either positive or negative.

The first possible solution is when the value inside the absolute value is positive.
$a = 2$

The second possible solution is when the value inside the absolute value is negative.
$a = -2$
Therefore, the solutions to the equation $2|a| - 1 = 3$ are $a = 2$ and $a = -2$ .