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Chapter 2: Problem 29

Solve using the addition principle. Don't forget to check! $$ -5+t=-9 $$

Short Answer

Expert verified
t = -4. Substituting -4 back into the original equation verifies the solution is correct.

Step by step solution

01

Isolate the variable

To isolate the variable, we want to get rid of the constant next to it. Here, we have -5 + t = -9 and we want to isolate t. Therefore, we need to add 5 to both sides of the equation.
02

Perform the addition

Add 5 to both sides of the equation: -5 + t + 5 = -9 + 5 Simplify both sides: t = -4
03

Check the solution

Substitute t = -4 back into the original equation to ensure the left and right sides are equal: -5 + (-4) = -9 Simplify: -9 = -9 Since both sides are equal, the solution is correct.

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Key Concepts

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

Solving Linear Equations
Linear equations are mathematical statements that involve variables with no exponents or powers. They're called 'linear' because they graph as straight lines. Solving them means finding the value of the variable that makes the equation true. Generally, linear equations take the form \( ax + b = c \). Here, solving involves isolating the variable to one side of the equation and balancing both sides.
Isolating the Variable
Isolating the variable means getting the variable by itself on one side of the equation. In the given exercise -5 + t = -9, we want to achieve this by removing the -5 from the left-hand side. To do that, we use the addition principle. The addition principle states that the same value can be added to both sides of an equation without changing the equation's balance. By adding 5 to both sides, we eliminate the -5 next to t, giving us a simplified form: \( t = -4 \). This makes t the subject of the equation.
Checking Solutions
Once we find a solution, it's crucial to verify it. This process ensures our solution makes the original equation true. For the given problem, substituting t = -4 back into the original equation -5 + t = -9, we get -5 + (-4). Simplifying this, we obtain -9. Since both sides of the equation equal -9, our solution is correct. Always take this step to confirm your work and ensure accuracy.

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Most popular questions from this chapter

Use an inequality and the five-step process to solve each problem. Musclebound Movers charges \(\$ 85\) plus \(\$ 40\) per hour to move households across town. Champion Moving charges \(\$ 60\) per hour for crosstown moves. For what lengths of time is Champion more expensive?

To prepare for Section \(2.6,\) review inequalities. Write a second inequality with the same meaning. $$5>y$$

Use an inequality and the five-step process to solve each problem. In order to qualify for a batting title, a major-league baseball player must average at least 3.1 plate appearances per game. For the first nine games of the season, a player had \(5,1,4,2,3,4,4,3,\) and 2 plate appearances. How many plate appearances must the player have in the tenth game in order to average at least 3.1 per game?

Use an inequality and the five-step process to solve each problem. The women's volleyball team can spend at most \(\$ 450\) for its awards banquet at a local restaurant. If the restaurant charges a \(\$ 40\) setup fee plus \(\$ 16\) per person, at most how many can attend?

Use an inequality and the five-step process to solve each problem. The formula \(R=-0.0026 t+4.0807\) can be used to predict the world record, in minutes, for the 1500 -m run tyears after \(1900 .\) Determine (in terms of an inequality) those years for which the world record will be less than \(3.8 \mathrm{min}\)
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