Explanation Given Information: The provided equation is 4 x + 3 15 − 2 x − 3 9 = 6 x + 4 6 − x . Formula used: Subtraction property: The resultant equation will be equivalent to the original equation, if the same quantity will subtracted to both sides of the equation. Division property: The resultant equation will be equivalent to the original equation, if the same non-zero quantity is divided on both sides of the equation. There are following steps to solve an equation with fractions. Step 1: Obtain the least common denominator (LCD) of all the fractional terms on both sides of the given equation. Step 2: Multiply both sides of the equation by the LCD to convert the provided equation without fractions. Step 3: Remove the parentheses (if any) by applying the distributive property. For any real numbers a , b , c , a ( b + c ) = a b + a c . Calculation: Consider the provided equation. 4 x + 3 15 − 2 x − 3 9 = 6 x + 4 6 − x Find the LCD of the denominators. The LCD of 6, 9 and 15 is 90. Multiply both sides of the equation by 90. 90 [ 4 x + 3 15 − 2 x − 3 9 ] = 90 [ 6 x + 4 6 − x ] Now, apply the distributive property on both sides of the equation. 90 ( 4 x + 3 15 ) − 90 ( 2 x − 3 9 ) = 90 ( 6 x + 4 6 ) − 90 x 6 ( 4 x + 3 ) − 10 ( 2 x − 3 ) = 15 ( 6 x + 4 ) − 90 x Again, apply the distributive property on both sides of the equation. 6 ( 4 x + 3 ) − 10 ( 2 x − 3 ) = 15 ( 6 x + 4 ) − 90 x 24 x + 18 − 20 x + 30 = 90 x + 60 − 90 x 4 x + 48 = 60 Apply the subtraction property stated above, subtract both sides of the equation by 48 . 4 x + 48 − 48 = 60 − 48 4 x = 12 Apply the division property stated above, divide both sides of the equation by 4

Bundle: Elementary Technical Mathematics, Loose-leaf Version, 12th + WebAssign Printed Access Card, Single-Term

12th Edition

ISBN: 9781337890199

Author: Dale Ewen

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Videos

Question

Chapter 6.4, Problem 22E

To determine

To calculate: The solution of the equation 4x+315−2x−39=6x+46−x and check it.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 21E

Chapter 6.4, Problem 23E

Students have asked these similar questions

(a) Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%. Assume that the five planning scenarios in the Hauck Financial rvices model are equally likely to occur. Hint: Modify model (8.10)-(8.19). Define a variable d, for each scenario and let d₂ > R - R¸ with d ≥ 0. Then make the objective function: Min Let FS = proportion of portfolio invested in the foreign stock mutual fund IB = proportion of portfolio invested in the intermediate-term bond fund LG = proportion of portfolio invested in the large-cap growth fund LV = proportion of portfolio invested in the large-cap value fund SG = proportion of portfolio invested in the small-cap growth fund SV = proportion of portfolio invested in the small-cap value fund R = the expected return of the portfolio R = the return of the portfolio in years. Min s.t. R₁ R₂ = R₁ R R5 = FS + IB + LG + LV + SG + SV = R₂ R d₁ =R- d₂z R- d₂ ZR- d₁R- d≥R- R = FS, IB, LG, LV, SG, SV…

The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas. The following is a linear program used to determine which cities Martin-Beck should construct a plant in. Let y₁ = 1 if a plant is constructed in Detroit; 0 if not y₂ = 1 if a plant is constructed in Toledo; 0 if not y₂ = 1 if a plant is constructed in Denver; 0 if not y = 1 if a plant is constructed in Kansas City; 0 if not. The variables representing the amount shipped from each plant site to each distribution center are defined just as for a transportation problem. *,, = the units shipped in thousands from plant i to distribution center j i = 1 (Detroit), 2 (Toledo), 3 (Denver), 4 (Kansas City), 5 (St.Louis) and…

Consider the following mixed-integer linear program. Max 3x1 + 4x2 s.t. 4x1 + 7x2 ≤ 28 8x1 + 5x2 ≤ 40 x1, x2 ≥ and x1 integer (a) Graph the constraints for this problem. Indicate on your graph all feasible mixed-integer solutions. On the coordinate plane the horizontal axis is labeled x1 and the vertical axis is labeled x2. A region bounded by a series of connected line segments, and several horizontal lines are on the graph. The series of line segments connect the approximate points (0, 4), (3.889, 1.778), and (5, 0). The region is above the horizontal axis, to the right of the vertical axis, and below the line segments. At each integer value between 0 and 4 on the vertical axis, a horizontal line extends out from the vertical axis to the series of connect line segments. On the coordinate plane the horizontal axis is labeled x1 and the vertical axis is labeled x2. A region bounded by a series of connected line segments, and several…

Chapter 6 Solutions

Bundle: Elementary Technical Mathematics, Loose-leaf Version, 12th + WebAssign Printed Access Card, Single-Term

Ch. 6.1 - Solve each equation and check: x+2=8 Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Solve each equation and check: 23n=6 Ch. 6.1 - Solve each equation and check: w712=3 Ch. 6.1 - Prob. 6E Ch. 6.1 - Solve each equation and check: x13=1.5 Ch. 6.1 - Solve each equation and check: n+12=5 Ch. 6.1 - Solve each equation and check: 3b=15.6 Ch. 6.1 - Solve each equation and check: y17=25

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The solution of the equation 4 x + 3 15 − 2 x − 3 9 = 6 x + 4 6 − x and check it.

Solution Summary: The author explains how to solve an equation with tions by obtaining the least common denominator of all the tional terms on both sides of the equation.

Concept explainers

Videos

To calculate: The solution of the equation 4x+315−2x−39=6x+46−x and check it.

Want to see the full answer?

Chapter 6 Solutions