Problem 97 Solve each equation. $$ -3 x... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 2: Problem 97

Solve each equation. $$ -3 x=\frac{1}{4} $$

Short Answer

Expert verified

x = -\frac{1}{12}

Step by step solution

- Isolate the variable

To solve for the variable, start by isolating the variable on one side of the equation. In this equation, we need to isolate the variable x. The equation is $ -3x = \frac{1}{4} $.

- Divide both sides by the coefficient of x

To isolate x, divide both sides of the equation by -3. This gives: \[ x = \frac{\frac{1}{4}}{-3} \].

- Simplify the fraction

Simplify the right side of the equation: \[ x = \frac{1}{4} \times \frac{1}{-3} = \frac{1}{-12} = -\frac{1}{12} \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolate the Variable

The first step in solving a linear equation is to isolate the variable. In other words, we want to get the variable (in this case, x) alone on one side of the equation. This often involves moving other terms to the opposite side. For the equation $-3x = \frac{1}{4}$, we need x alone on the left side. We do this by addressing everything that is around x to isolate it easily.

Divide by Coefficient

After isolating the variable, our next move is to get rid of the coefficient attached to it. A coefficient is a number that is multiplied by the variable. In the equation $-3x = \frac{1}{4}$, -3 is the coefficient of x. To solve for x, divide both sides of the equation by -3. This helps eliminate the effect of the coefficient on the variable. The division leads to the expression: \[ x = \frac{\frac{1}{4}}{-3} \].

Simplify Fractions

The final step is to simplify the fraction. When we have a fraction on the right side, we need to make it as simple as possible. From the prior step, we have $\frac{\frac{1}{4}}{-3}$. Multiplying fractions requires multiplying the numerators together and the denominators together: \[ x = \frac{1}{4} \times \frac{1}{-3} \]. This simplifies to $\frac{1}{-12}$, which we can further simplify to $-\frac{1}{12}$. Thus, x equals $-\frac{1}{12}$.

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91影视

Solve each equation. $$ -3 x=\frac{1}{4} $$

Short Answer

Step by step solution

- Isolate the variable

- Divide both sides by the coefficient of x

- Simplify the fraction

Key Concepts

Isolate the Variable

Divide by Coefficient

Simplify Fractions

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