Problem 287 Solve each linear equation. $$... [FREE SOLUTION]

Chapter 2: Problem 287

Solve each linear equation. $$4(2.5 v-0.6)=7.6$$

Short Answer

Expert verified

The solution to the equation is $v = 1$.

Step by step solution

Distribute the 4

Multiply 4 by each term inside the parenthesis: $4(2.5v - 0.6) = 7.6$. This gives us: $4 \times 2.5v - 4 \times 0.6 = 7.6$, or $10v - 2.4 = 7.6$.

Isolate the Variable Term

Add 2.4 to both sides of the equation to isolate the variable term: $10v - 2.4 + 2.4 = 7.6 + 2.4$. Simplifying this gives us: $10v = 10$.

Solve for v

Divide both sides by the coefficient of $v$, which is 10: $\frac{10v}{10} = \frac{10}{10}$. Simplifying this gives us: $v=1$.

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Key Concepts

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

Distributive Property

The distributive property is a key tool in algebra that helps break down complex expressions. It states that a number multiplied by a sum or difference inside parentheses can be distributed to each term separately. In simpler terms, if you have something like $a(b + c)$, it can be broken down into $ab + ac$.
In our exercise, we started with $4(2.5v - 0.6) = 7.6$. To apply the distributive property, we multiplied 4 by both $2.5v$ and $-0.6$.

4 脳 2.5v = 10v
4 脳 -0.6 = -2.4

So, the expression $4(2.5v - 0.6)$ transforms into $10v - 2.4$. The distributive property helps simplify the equation, making it easier to solve.

Isolating Variables

Isolating the variable means manipulating the equation so that the variable (in this case, $v$) is by itself on one side of the equation. This is a critical step in solving linear equations. Starting from our simplified equation $10v - 2.4 = 7.6$, we need to get $10v$ by itself.
To do this, we add 2.4 to both sides of the equation. This 'undoes' the subtraction of 2.4:

$10v - 2.4 + 2.4 = 7.6 + 2.4$
Simplifies to $10v = 10$

Now, $v$ is almost isolated; it is just being multiplied by 10, which is a simpler issue to tackle in the final step.

Solving for a Variable

Once the variable has been isolated into a simpler expression, the next step is to actually solve for it. In our equation, we now have $10v = 10$. To solve for $v$, we divide both sides by the coefficient of $v$, which is 10. This step helps in getting the variable alone without any coefficients:

$\frac{10v}{10} = \frac{10}{10}$
Which simplifies to $v = 1$

Dividing both sides by the same number ensures that the equality holds true and lets us find the value of the variable. Always double-check your work to make sure no mistakes were made in earlier steps.

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91影视

Solve each linear equation. $$4(2.5 v-0.6)=7.6$$

Short Answer

Step by step solution

Distribute the 4

Isolate the Variable Term

Solve for v

Key Concepts

Distributive Property

Isolating Variables

Solving for a Variable

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