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Chapter 3: Problem 294

In the following exercises, solve for the unknown. $$ v-7=-8 $$

Short Answer

Expert verified
v = -1

Step by step solution

01

Identify the equation

The equation given is: v - 7 = -8
02

Isolate the variable

To solve for the unknown variable v, add 7 to both sides of the equation to cancel out the -7 on the left side.
03

Simplify both sides

Adding 7 to both sides, the equation becomes: v - 7 + 7 = -8 + 7 Simplifying both sides results in: v = -1

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Key Concepts

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

isolating variables
Isolating variables is a key step in solving linear equations. The aim is to get the unknown variable on one side of the equation by itself.
In the given problem, the equation is: \( v - 7 = -8 \)
To isolate the variable \( v \), add 7 to both sides. This cancels out the \( -7 \) on the left side.

Once we do that, the equation becomes: \( v - 7 + 7 = -8 + 7 \).
Simplifying this step by step, we get: \( v = -1 \). Now the variable is isolated, and the value of \( v \) is found.
simplifying equations
Simplifying equations involves making them easier to work with by combining like terms and performing arithmetic operations.
In our example, when we added 7 to both sides, we performed a simplification:
  • \( v - 7 + 7 \) simplifies to \( v \)
  • \( -8 + 7 \) simplifies to \( -1 \)

By simplifying, we make the equation more straightforward and easier to solve.
basic algebra
Basic algebra consists of fundamental operations and principles used to manipulate mathematical expressions and equations.
One of these fundamental operations is solving for an unknown. We do this by performing the same operation on both sides of the equation.
In the provided example, the operation was addition. By adding 7 to both sides, we maintained the balance of the equation and simplified it step by step.
Remember:
  • Always perform the same operation on both sides
  • Simplify in small steps
  • Isolate the variable before solving
These principles are foundational for handling more complex algebraic equations later on.

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Most popular questions from this chapter

In the following exercises, simplify each expression. $$ (8-15)(9-3) $$

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