Explanation Given Information: The provided equation is 3 x 5 − 9 − 3 x 10 = 6 10 − 3 x + 6 10 . 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. 3 x 5 − 9 − 3 x 10 = 6 10 − 3 x + 6 10 3 x 5 − 9 − 3 x 10 = 6 10 − 3 x + 6 10 Find the LCD of the denominators. The LCD of 5 and 10 is 10. Multiply both sides of the equation by 10. 10 [ 3 x 5 − 9 − 3 x 10 ] = 10 [ 6 10 − 3 x + 6 10 ] Now, apply the distributive property on both sides of the equation. 10 ( 3 x 5 ) − 10 ( 9 − 3 x 10 ) = 10 ( 6 10 ) − 10 ( 3 x + 6 10 ) 2 ( 3 x ) − 1 ( 9 − 3 x ) = 1 ( 6 ) − ( 3 x + 6 ) 6 x − 9 + 3 x = 6 − 3 x − 6 9 x − 9 = − 3 x Apply the subtraction property stated above, subtract both sides of the equation by 9 x . 9 x − 9 − 9 x = − 3 x − 9 x − 12 x = − 9 Apply the division property stated above, divide both sides of the equation by − 12 . − 12 x − 12 = − 9 − 12 x = 3 4 Check: Substitute 3 4 for x in the original equation

11th Edition

ISBN: 9781285199191

Author: Dale Ewen, C. Robert Nelson

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 24E

To determine

To calculate: The solution of the equation 3x5−9−3x10=610−3x+610 and check it.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 23E

Chapter 6.4, Problem 25E

Students have asked these similar questions

Q/(a)Let X be a finite dimension vector space over a field F and S₁,S2CX such that S₁SS2. Show that whether (1) if S, is a base for X then base for X or not (2) if S2 is a base for X then S, is a base for X or not (b) Show that every subspace of vector space is convex and affine set but the conevrse need not to be true. allet M be a non-empty subset of a vector space X over a field F and x,EX. Show that M is a hyperspace iff xo+ M is a hyperplane and xo€ xo+M. bState Hahn-Banach theorem and write with prove an application about it. Show that every singleten subset and finite subset of a normed space is closed. Oxfallet f he a function from a normad roace YI Show tha ir continuour aty.GYiff

arc. Consider the network of Figure 2, where the capacities of arcs are given in rectangles at each (i) Knowing that (W, W) with W = network. {s, a, b, c} is a minimal s- t cut suggest a maximal flow for this

Consider the problem of minimising the Euclidean distance from the point (-4,5) in the plane to the set of points (x, y) that have integer coordinates and satisfy the inequality: x2 y² + ≤1. 4 9 (a) Use an exhaustive search to solve this problem. (b) Use a local search method to solve this problem. First, define the search space and the neighbourhood. Then, attempt to find the minimum starting from the initial point (x, y) = (2,0). The neighbourhood of a point should contain at least two distinct points but must not encompass the entire feasible search space. Will your local search method find the global optimum?

Chapter 6 Solutions

Elementary Technical Mathematics

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 3 x 5 − 9 − 3 x 10 = 6 10 − 3 x + 6 10 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 3x5−9−3x10=610−3x+610 and check it.

Want to see the full answer?

Chapter 6 Solutions