Answer x = 5 Explanation Given: 7 = 2 x − 3 Concept Used: Steps to solve a linear equation: Use distributive property to eliminate any grouping symbol. Simplify the expression in each side of the equation. Collect the variables on one side of the equation and the constants on the other side. Isolate the variable To check the solution of an equation substitute the solution in the equation and check whether it satisfies. Calculation: In order to solve the equation: 7 = 2 x − 3 Isolate the variable by first adding 3 both sides, as 7 = 2 x − 3 ⇒ 7 + 3 = 2 x − 3 + 3 ⇒ 10 = 2 x − 0 ⇒ 10 = 2 x ⇒ 2 x = 10 Now, further simplify this by dividing both sides by 2. 2 x = 10 ⇒ 2 x 2 = 10 2 ⇒ x = 5 Thus, solution of given equation is x = 5 , and this satisfies that x ∈ { 0 , 1 , 2 , 3 , 4 , 5 , 6 } .

(REV)00 Edition

ISBN: 9780395977224

Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher: McDougal Littell

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Question

Chapter 1.6, Problem 6MRE

To determine

To solve: the equation:

7=2x−3

Where, x∈{0,1,2,3,4,5,6} .

Expert Solution & Answer

Answer to Problem 6MRE

x=5

Explanation of Solution

Given:

7=2x−3

Concept Used:

Steps to solve a linear equation:

Use distributive property to eliminate any grouping symbol.
Simplify the expression in each side of the equation.
Collect the variables on one side of the equation and the constants on the other side.
Isolate the variable

To check the solution of an equation substitute the solution in the equation and check whether it satisfies.

Calculation:

In order to solve the equation:

7=2x−3

Isolate the variable by first adding 3 both sides, as

7=2x−3⇒7+3=2x−3+3⇒10=2x−0⇒10=2x⇒2x=10

Now, further simplify this by dividing both sides by 2.

2x=10⇒2x2=102⇒x=5

Thus, solution of given equation is x=5 , and this satisfies that x∈{0,1,2,3,4,5,6} .

Chapter 1.6, Problem 5MRE

Chapter 1.6, Problem 7MRE

Chapter 1 Solutions

Algebra: Structure And Method, Book 1

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