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Chapter 8: Problem 99

In the following exercises, solve the equation. $$-18-7=5 t-9 t-6 t$$

Short Answer

Expert verified
t = 2.5

Step by step solution

01

Simplify the Equation

First, simplify the equation by combining like terms on the right-hand side: \(-18 - 7 = 5t - 9t - 6t\)
02

Combine Like Terms

Combine the terms involving \(t\) on the right-hand side: \(5t - 9t - 6t = (5 - 9 - 6)t = -10t\).So, the equation becomes:\(-18 - 7 = -10 t\)
03

Simplify the Left-hand Side

Simplify the left-hand side of the equation: \(-18 - 7 = -25\).Now, we have:\(-25 = -10t\)
04

Solve for t

Isolate \(t\) by dividing both sides of the equation by \(-10\): \(t = \frac{-25}{-10}\).Simplify the fraction: \(t = 2.5\)

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Key Concepts

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

Equation-solving Steps
The process to solve any linear equation involves several steps. Let鈥檚 break them down:
  • Simplify: First, look at both sides of the equation and combine like terms.
  • Rewrite: Ensure the equation is in a standard format, often \( ax + b = c \).
  • Isolate: Work on isolating the variable you鈥檙e solving for. This can involve addition, subtraction, multiplication, or division.
  • Solution Checking: Always substitute your answer back into the original equation to verify its correctness.

    • Each of these steps allows for a clear strategy to efficiently address and solve the equation, leading to precise results.

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