Problem 71 Solve the equation. $$5 x-2 x=... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 71

Solve the equation. $$5 x-2 x=-15$$

Short Answer

Expert verified

The solution to the equation is $x = -5$.

Step by step solution

Combine Like Terms

First, simplify the left side of the equation by combining like terms: \[5x - 2x = 3x\].So the equation becomes:\[3x = -15\].

Isolate the Variable

Next, isolate the variable by dividing both sides of the equation by the coefficient of $x$, which is 3:\[x = \frac{-15}{3}\].

Simplify the Fraction

Finally, simplify the fraction on the right side of the equation:\[x = -5\].

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Key Concepts

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

Combine Like Terms

To solve equations efficiently, you need to combine like terms. Like terms have the same variables raised to the same power. For example, in \[5x - 2x\], both terms are 'like' because they contain the variable $x$. Combining them means adding or subtracting their coefficients (the numbers in front of the variables).

Here, combine the coefficients: \[5x - 2x = 3x.\]
This makes the equation simpler:

\[3x = -15\].

Remember that combining like terms helps reduce the complexity of the equation, making it easier to solve.

Isolate the Variable

Once you've combined like terms, the next step is to isolate the variable to one side of the equation. This means getting the variable $x$ alone by performing operations that 'reverse' the effects of adding, subtracting, or multiplying by other numbers.

In the equation \[3x = -15\]:
1. Notice that $x$ is multiplied by 3.
2. To undo this, divide both sides of the equation by 3:
\[ 3x \div 3 = -15 \div 3 \rightarrow x = -5 \].

Isolating the variable helps find the value of $x$. When you perform the same operation to both sides of the equation, \[ x = -5 \]

Simplify Fractions

The final step is to simplify fractions. This process makes the equation's solutions more understandable. In the context of our exercise:
\[x = \frac{-15}{3} \]
you need to simplify the fraction.

Simplifying a fraction means reducing it to its simplest form. Divide the numerator and the denominator by their greatest common factor (GCF).

- Here, the GCF of -15 and 3 is 3.
-Divide both parts by 3:
\[\frac{-15}{3} = -5\]

So, we get:
\[ x = -5 \]
Simplifying fractions helps keep your equations neat and your solutions clear.

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91影视

Solve the equation. $$5 x-2 x=-15$$

Short Answer

Step by step solution

Combine Like Terms

Isolate the Variable

Simplify the Fraction

Key Concepts

Combine Like Terms

Isolate the Variable

Simplify Fractions

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