Questions: Solve the following for x: 3x-5=10

Transcript text: 8. Solve the following for $x:|3 x-5|=10$

Solution

Solution Steps

To solve the equation $|3x - 5| = 10$, we need to consider the definition of absolute value. This equation can be split into two separate linear equations: $3x - 5 = 10$ and $3x - 5 = -10$. Solving each of these equations will give us the possible values for $x$.

Step 1: Set Up the Equations

To solve the equation $|3x - 5| = 10$, we consider the definition of absolute value, which leads to two separate linear equations:

$3x - 5 = 10$
$3x - 5 = -10$

Step 2: Solve the First Equation

Solve the equation $3x - 5 = 10$: \[ 3x - 5 = 10 \implies 3x = 15 \implies x = \frac{15}{3} = 5 \]

Step 3: Solve the Second Equation

Solve the equation $3x - 5 = -10$: \[ 3x - 5 = -10 \implies 3x = -5 \implies x = \frac{-5}{3} \]

Final Answer

The solutions to the equation $|3x - 5| = 10$ are: \[ \boxed{x = 5} \quad \text{and} \quad \boxed{x = -\frac{5}{3}} \]

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