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Chapter 2: Problem 39

\(6 t-2=5 t\)

Short Answer

Expert verified
t = 2

Step by step solution

01

Move all terms involving t to one side

Subtract \(5t\) from both sides to isolate the variable \(t\). This gives: \(6t - 5t - 2 = 0\).
02

Simplify the equation

Combine like terms: \(\:6t - 5t = t\), resulting in \(t - 2 = 0\).
03

Solve for t

Add 2 to both sides to isolate \(t\): \(t - 2 + 2 = 0 + 2\). This simplifies to \(t = 2\).

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Key Concepts

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

Solving Linear Equations
Solving linear equations is a fundamental skill in algebra. A linear equation is an equation where the highest power of the variable is one. For example, let's take the equation from the exercise: (6t - 2 = 5t). Our goal is to find the value of t that makes the equation true.

To solve a linear equation, follow these general steps:
  • Move all terms involving the variable to one side of the equation.
  • Move all constant terms to the other side of the equation.
  • Simplify both sides, if necessary.
  • Isolate the variable and solve for it.
Isolating Variables
Isolating the variable is an essential step in solving linear equations. It means getting the variable by itself on one side of the equation. Let's revisit the given exercise: (6t - 2 = 5t).

First, we need to isolate t by moving all terms involving t to one side.
We do this by subtracting 5t from both sides: (6t - 5t - 2 = 0).Now the equation has all the t terms on one side.

The goal is to have the variable t on one side of the equation and everything else on the other side, so we can solve for t easily.
Combining Like Terms
Combining like terms simplifies the equation and makes it easier to solve. In the equation (6t - 5t - 2 = 0), we have two t terms: (6t) and (5t). These are like terms because they both have the variable t.

Subtracting 5t from 6t gives us: (6t - 5t = t). Now the equation is simpler: (t - 2 = 0).

To finish solving, we isolate t by adding 2 to both sides: (t - 2 + 2 = 0 + 2), which simplifies to (t = 2).

Combining like terms helps reduce the equation to its simplest form, making it easier to solve for the variable.

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Most popular questions from this chapter

Beyonc茅 and Guns \(\mathrm{N}\) ' Roses had the two top-grossing concert tours for 2016 , together generating \(\$ 300\) million in ticket sales. Guns \(\mathrm{N}\) ' Roses took in \(\$ 38\) million less than Beyonc茅. How much did each tour generate? (Data from Pollstar.)

When \(\frac{2}{3}\) of a number is added to \(10,\) the result is 5 more than the number. Find the number.

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If 3 is added to a number and this sum is doubled, the result is 2 more than the number. Find the number.

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