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Chapter 2: Problem 37

Solve each equation, and check your solution. $$ -4 x+7=-5 x+9 $$

Short Answer

Expert verified
x = 2

Step by step solution

01

- Combine Like Terms

Start by combining the like terms from both sides of the equation. Add 5x to both sides to get all terms involving x on one side: -4x + 5x + 7 = 9
02

- Simplify the Equation

Simplify the equation by combining the x terms: x + 7 = 9
03

- Isolate x

Subtract 7 from both sides to isolate x: x = 9 - 7 x = 2
04

- Check the Solution

Substitute x back into the original equation to verify: -4(2) + 7 = -5(2) + 9 -8 + 7 = -10 + 9 -1 = -1 The solution x=2 is correct.

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Key Concepts

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

Combining Like Terms
Combining like terms is a fundamental concept in solving linear equations. It means you add or subtract terms that have the same variable. This simplifies the equation, allowing you to solve it more easily.

In our equation, we start with -4x + 7 = -5x + 9.
Notice both sides of the equation have terms containing 'x'.
By adding 5x to both sides, we get:
-4x + 5x + 7 = 9.
This step gathers all 'x' terms on one side, making it easier to combine them and simplify the equation.
Simplification gives us: x + 7 = 9. Now, the equation is ready for isolating the variable.
Isolating Variables
Isolating the variable is crucial for solving the equation. Here you need to get 'x' on one side by itself.

From our simplified equation x + 7 = 9, we need to remove the 7 from the left side.
To do this, subtract 7 from both sides: x + 7 - 7 = 9 - 7.
This reduces the equation to x = 2.
Now, we've successfully isolated 'x'.
The solution to the equation is now clear: x = 2.
Checking Solutions
Checking your solution ensures your answer is correct. You substitute the solution back into the original equation to verify it satisfies both sides.

We found x = 2.
Substitute 2 back into the original equation: -4(2) + 7 = -5(2) + 9.
Calculate each side: -8 + 7 = -10 + 9.
This simplifies further to: -1 = -1.
Both sides are equal, confirming our solution is accurate.
Hence, x = 2 is indeed the correct solution for the equation.

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Most popular questions from this chapter

The formula for converting Celsius temperature to Fahrenheit is $$F=\frac{9}{5} C+32$$ The Fahrenheit temperature of Phoenix has never exceeded \(122^{\circ} .\) How would you describe this using Celsius temperature?

Write an equation using the information given in the problem. Use \(x\) as the variable. Then solve the equation. If twice a number is divided by \(5,\) the result is \(4 .\) Find the number.

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