/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 24 Solve. $$ 5 a-11=24 $$... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 24

Solve. $$ 5 a-11=24 $$

Short Answer

Expert verified
The solution is \(a = 7\).

Step by step solution

01

- Add 11 to Both Sides

To isolate the term with the variable, add 11 to both sides of the equation: \(5a - 11 + 11 = 24 + 11\)This simplifies to:\(5a = 35\)
02

- Divide by 5

Now, divide both sides by 5 to solve for \(a\): \(\frac{5a}{5} = \frac{35}{5}\)This simplifies to:\(a = 7\)

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Key Concepts

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

Variable Isolation
To solve linear equations, we aim to isolate the variable. This means we want to get the variable by itself on one side of the equation. In our example, the variable is **'a'**. Initially, we have the equation \[ 5a - 11 = 24 \]The term with the variable 'a' is **5a**. Our goal is to perform operations that leave **'a'** alone. Isolating the variable will help us find its true value.
Addition Property of Equality
One of the essential tools when solving equations is the **Addition Property of Equality**. This property states that if you add the same number to both sides of an equation, the equation remains balanced. For our problem, we started with:\[ 5a - 11 = 24 \]To isolate **5a**, we need to eliminate the -11. We achieve this by adding 11 to both sides:\[ 5a - 11 + 11 = 24 + 11 \]This operation simplifies our equation to:\[ 5a = 35 \]Notice that subtracting 11 and adding 11 cancels each other out (because -11 + 11 = 0), leaving **5a** alone on the left side.
Division Property of Equality
After applying the Addition Property of Equality, we isolate the term with the variable to get:\[ 5a = 35 \]Now, we use the **Division Property of Equality**, which states you can divide both sides of an equation by the same nonzero number, and the equation will still hold true. Since **5a** means 5 times 'a', we divide both sides by 5 to solve for 'a':\[ \frac{5a}{5} = \frac{35}{5} \]Simplifying this, we get:\[ a = 7 \]So, dividing by 5 helps us determine that the value of 'a' that satisfies the equation is 7. By understanding and using these properties, we can solve linear equations step-by-step systematically.

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Most popular questions from this chapter

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \sqrt{10} \in \mathbb{R} $$

Write an equivalent expression using an associative law. $$ -7(a b) $$

Translate to an algebraic expression. \(\\{x | x=3 n, n \text { is a natural number }\\}\)

Use set-builder notation to write each set. The set of all multiples of 5 between 7 and 79

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ \frac{8 \div 4 \cdot 6\left|4^{2}-5^{2}\right|}{9-4+11-4^{2}} $$
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