Textbook Question
In Exercises 1–34, solve each rational equation. If an equation has no solution, so state.1/x + 2 = 3/x
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1. Equations & Inequalities
Linear Equations
1:33 minutesProblem 3
Textbook Question
In Exercises 1–26, solve and check each linear equation. 7x - 5 = 72
Verified step by step guidance1
Start with the given linear equation: \$7x - 5 = 72$.
Add 5 to both sides of the equation to isolate the term with \(x\): \$7x - 5 + 5 = 72 + 5\( which simplifies to \)7x = 77$.
Divide both sides of the equation by 7 to solve for \(x\): \(\frac{7x}{7} = \frac{77}{7}\) which simplifies to \(x = 11\).
Check your solution by substituting \(x = 11\) back into the original equation: \$7(11) - 5$.
Simplify the left side to verify it equals 72: \$77 - 5 = 72\(, confirming that \)x = 11$ is the correct solution.
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1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Linear Equations
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. It forms a straight line when graphed and typically has the form ax + b = c. Solving linear equations involves finding the value of the variable that makes the equation true.
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Isolating the Variable
To solve a linear equation, you must isolate the variable on one side of the equation. This involves performing inverse operations such as addition, subtraction, multiplication, or division to both sides, maintaining equality. For example, to solve 7x - 5 = 72, add 5 to both sides before dividing by 7.
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Checking the Solution
After finding the value of the variable, substitute it back into the original equation to verify the solution. This ensures that the left and right sides of the equation are equal, confirming the correctness of the solution. Checking helps avoid errors made during the solving process.
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