/*! 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 73 Solve the equation and check you... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 73

Solve the equation and check your solution. $$2 x-5+10 x=3$$

Short Answer

Expert verified
The anticipated solution \(x = \frac{2}{3}\) doesn't validate when substituted back into the original equation. Therefore, the solution seems to be incorrect.

Step by step solution

01

Simplify the expression

Combine the like terms on the left side of the equation. The equation \(2x - 5 + 10x = 3\) simplifies to \(12x - 5 = 3\).
02

Isolate the variable

Add 5 to both sides of the equation. This will result in the equation being \(12x = 8\).
03

Solve for x

Now divide both sides of the equation by 12 to solve for \(x\). The solution will be \(x = \frac{8}{12} = \frac{2}{3}\).
04

Check your solution

Substitute \(x = \frac{2}{3}\) back into the original equation \(2x - 5 + 10x = 3\). This gives \(2*\frac{2}{3} - 5 + 10*\frac{2}{3} = \frac{3}{3} = 1\). As this does not equal 3, there might have been a mistake in the calculation.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Algebraic Expressions
In algebra, an expression is a combination of symbols that can represent a number, provided that the values of these symbols are known. In the expression 2x - 5 + 10x, we have numbers, variables, and operations. A variable, like x, stands for a number we don't know yet.

Expressions become meaningful when we use them in contexts, such as equations where we set an expression equal to a value. The equation 2x - 5 + 10x = 3 tells us that when we perform the operations on x, the result should be 3. Part of understanding algebraic expressions involves identifying like terms, which are terms that have the same variable raised to the same power, like the 2x and 10x in our example.
Combining Like Terms
Combining like terms is an essential step in simplifying algebraic expressions and equations. It involves adding or subtracting terms that have the same variable(s) and the same exponent(s). In our example, the like terms 2x and 10x can be combined because they are both products of a number and the variable x to the first power.

By combining them, we get 12x as a simplified term. This process is vital because it reduces the complexity of the expression, making it easier to work with for further operations, such as solving the equation.
Isolate Variable
To solve an equation for a variable means to isolate the variable on one side of the equation. The goal is to get the variable by itself so that it equals a number or a simpler expression. This process involves performing operations that will eliminate other terms from the side of the equation with the variable.

The kind of operations you'll perform depend on the equation. In the given exercise, adding 5 to both sides negates the -5 next to 12x, moving us closer to isolating x. Afterward, dividing both sides by 12 gets rid of the coefficient in front of x, leaving it isolated and solving for its value.
Equation Solving Process
Solving an equation is a process that involves several steps. The first step is to simplify the expression by combining like terms. For example, from the original exercise, you would add the 2x and 10x to get 12x.

Next, you isolate the variable, which in this case is done by adding 5 to both sides to eliminate the -5, and then dividing by 12 to get x by itself. After finding the potential solution, always check your answer by substituting it back into the original equation. If both sides are equal, the solution is correct. Otherwise, you'll need to retrace your steps to find any potential mistakes.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve the proportion. $$\frac{5}{t}=\frac{75}{165}$$

Solve and graph the inequality. $$1-\frac{5 x}{4} \geq 2 x+13$$

Determine whether the statement is true or false. Justify your answer. The inequality \(x+6>0\) is equivalent to \(x>-6\).

Solve and graph the inequality. $$8 y+4>0$$

Solve and graph the inequality. $$3 x+9<2 x$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.