Solve the following equations with decimals. 4.1 x + 2.4 = 3.6 x − ( − 4 ) 4.1x+2.4=3.6x-\left(-4\right)

Welcome back. In this problem, we wanna solve the equation 4.1 x plus 2.4 equals 3.6 x minus negative four. Now this equation has decimals, so we have to start with step zero, clearing those decimals by multiplying by a power of 10. We can check each of our terms and see how many decimal places it has. Then when we find the highest number, we'll multiply by that power of 10. Let's start on the left side of the equation. We have 4.1 x, and 4.1 has one decimal place. Next, we have 2.4, which also has one decimal place. On the right side of the equation, we have 3.6 x, and 3.6 has one decimal place. And finally, negative four has zero decimal places. So looking at our number of decimal places, we have one, one, one, and zero, so the highest number there is one, and we want to multiply by the first power of ten, ten to the first, which is just 10. So let's multiply both sides of our equation by 10. We get 10 times 4.1 x plus 2.4 is equal to 10 times 3.6 x minus negative four. Let's distribute that 10 on both sides of the equation. On the left side, we get 10 times 4.1 x first. Now when we multiply by 10, we move the decimal point one place to the right. So when we do 10 times 4.1, we move that decimal point one place to the right to get 41, and that becomes 41 x. Next, we multiply 10 by 2.4, and again, we move the decimal point one place to the right to get 24. On the right side of the equation, we'll do 10 times 3.6 x, and we move the decimal point one place to the right. 10 times 3.6 is 36, so that gets us 36 x. Next, we do 10 times negative four, which is minus 40, so we get minus negative 40. Now that we have no more decimals, step zero is all set and we move on to step one. This is a great time to simplify our minus negative 40. As a reminder, minus a negative is just a positive, so we can rewrite this as 41 x plus 24 is equal to 36 x plus 40. We don't have any more distributing or combining like terms we have to do, so step one is all set, and we can move on to step two. We wanna collect all of our variable terms on one side of the equation and all of our constant terms on the other side. Currently, we have variable and constant terms on both sides of the equation. So let's try to get variables to the left and constants to the right, starting with our constants. We need to get rid of this plus 24 on the left, so we can do that by subtracting 24 from both sides of the equation. It cancels on the left, leaving us with 41 x, and on the right side, we get 36 x plus 40 minus 24, which is plus 16. Next, we wanna get rid of the 36 x on the right so that all of our variable terms are on the left side of the equation. So we want to subtract 36 x from both sides of the equation. That's going to cancel on the right side of the equation, leaving us with 16. On the left side of the equation, we have 41 x minus 36 x, which is five x. Now that we have all of our variable terms on the left side of the equation and constants on the right, step two is all set, and we move on to step three where we want to isolate our variable. We need to get rid of this coefficient of five so we can divide both sides of the equation by five. It cancels the coefficient on the left side leaving us with x. On the right side, we can't simplify the fraction 16 fifths, so we get the solution x equals 16 fifths. When our equation has decimals, sometimes we like to express the answer as a decimal instead. We can get the decimal by doing 16 and dividing it by five, and if you do, you'll get x equals 3.2. Three point two and sixteen fifths are equal to each other, so both of these solutions are the same solution, just expressed in a different way. We can see that our variable is isolated, so step three is all set. For step four, you can choose one of these forms, 16 fifths or 3.2, and plug that value of x back into the original equation to verify our solution. But our solution is 16 fifths, which is equal to 3.2. Once you're all set checking, great job.

Table of contents

Skip topic navigation

1. Review of Real Numbers2h 43m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
44m

2. Linear Equations and Inequalities5h 35m

Solving Linear Equations
2h 23m

Linear Inequalities in One Variable
46m

Set Operations and Compound Inequalities
1h 7m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

3. Solving Word Problems2h 46m

Introduction to Problem Solving
37m

Formulas
25m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphs and Functions5h 12m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
53m

Function Notation
15m

Composition of Functions
17m

5. Systems of Linear Equations1h 53m

Solving Systems of Linear Equations by Graphing
29m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

Systems of Linear Inequalities
23m

6. Exponents, Polynomials, and Polynomial Functions3h 17m

The Product Rule
9m

The Quotient Rule
10m

Intro to the Power Rules
17m

The Power of a Quotient Rule
13m

Negative Exponents
24m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
38m

Special Products
34m

7. Factoring2h 49m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
41m

Quadratic Equations & Applications
41m

8. Rational Expressions and Functions3h 44m

Simplifying Rational Expressions
42m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

Direct & Inverse Variation
27m

9. Roots, Radicals, and Complex Numbers2h 33m

Introduction to Radical Expressions
11m

Simplifying Radical Expressions
27m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
23m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

10. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

11. Inverse, Exponential, & Logarithmic Functions1h 5m

Introduction to Inverse Functions
25m

Exponential Functions
13m

Introduction to Logarithmic Functions
26m

12. Conic Sections & Systems of Nonlinear Equations58m

Graphing Circles
32m

Ellipses
15m

Parabolas
10m

13. Sequences, Series, and the Binomial Theorem1h 51m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
29m

Factorials
13m

2. Linear Equations and Inequalities

Solving Linear Equations

Intermediate Algebra

2. Linear Equations and Inequalities

Solving Linear Equations

Previous problemNext problem

Struggling with Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Solve the following equations with decimals.
$4.1 x + 2.4 = 3.6 x - (- 4)$

$x=-12.8$

$x=$\frac{64}{77}$$

$x=80$

$x=3.2$

0 Comments

Previous problemNext problem

Verified step by step guidance

Start with the given equation: $4.1x + 2.4 = 3.6x - \left(-4\right)$.

Simplify the right side by removing the double negative: $3.6x - \left(-4\right) = 3.6x + 4$.

Rewrite the equation as \$4.1x + 2.4 = 3.6x + 4$.

Get all terms involving $x$ on one side by subtracting \$3.6x$ from both sides: $4.1x - 3.6x + 2.4 = 4$.

Isolate $x$ by subtracting \$2.4$ from both sides and then dividing both sides by the coefficient of $x$: $x = \frac{4 - 2.4}{4.1 - 3.6}$.

5:27m

Watch next

Master Solving Linear Equations with Fraction or Decimal Coefficients Example 7 with a bite sized video explanation from Patrick Ford

Struggling with Intermediate Algebra?

Solve the following equations with decimals.4.1x+2.4=3.6x−(−4)4.1x+2.4=3.6x-\(\left\)(-4\(\right\))

Watch next

Solve the following equations with decimals.
$4.1 x + 2.4 = 3.6 x - (- 4)$