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Radicals - Solve Equation










































show all steps in solving this radical expression..
(sqrt2x-3)=4

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Nov 23, 2011
Radicals - Solve Equation
by: Staff


Question:

show all steps in solving this radical expression..
(sqrt2x-3)=4


Answer:

Remember, the goal of the work you do in solving this equation is to put the x (all by itself) on one side of the equation, and everything else on the other side of the equation.

When you are finished, one side of the equation will look like this: x =


The placement of the parentheses in the problem statement makes the equation unclear. I will work it out for you in two different ways.


If you intend for the equation to be: sqrt(2x) - 3 = 4

sqrt(2x) - 3 = 4


to REMOVE THE 3 from the left side of the equation, add 3 to each side of the equation (you need to remove the 3 because your goal is to make the left hand side of the equation look like this: x =)


sqrt(2x) - 3 + 3 = 4 + 3

sqrt(2x) + 0 = 7

sqrt(2x) = 7


to REMOVE THE SQUARE ROOT SIGN from the left side of the equation, square each side of the equation (you need to remove the sqrt sign because your goal is to make the left hand side of the equation look like this: x =)


[sqrt(2x)]² = 7²

2x = 49


to REMOVE THE 2 from the left side of the equation, divide each side of the equation by 2 (you need to remove the 2 because your goal is to make the left hand side of the equation look like this: x =)

2x/2 = 49/2

x * (2/2) = 49/2

x * (1) = 49/2

x = 49/2

x = 24.5


the final answer is: x = 24.5



If you intend for the equation to be: sqrt(2x - 3) = 4

sqrt(2x - 3) = 4


to REMOVE THE SQUARE ROOT SIGN from the left side of the equation, square each side of the equation (you need to remove the sqrt sign because your goal is to make the left hand side of the equation look like this: x =)

[sqrt(2x - 3)]² = 4²

2x - 3 = 16


to REMOVE THE 3 from the left side of the equation, add 3 to each side of the equation (you need to remove the 3 because your goal is to make the left hand side of the equation look like this: x =)

2x - 3 + 3 = 16 + 3

2x + 0 = 19

2x = 19


to REMOVE THE 2 from the left side of the equation, divide each side of the equation by 2 (you need to remove the 2 because your goal is to make the left hand side of the equation look like this: x =)

2x/2 = 19/2

x * (2/2) = 19/2

x * (1) = 19/2

x = 19/2

x = 9.5


the final answer is: x = 9.5

-----------------------------------------------------------

check your work


If the equation is: sqrt(2x) - 3 = 4

x = 24.5

replace every x in the equation with 24.5

sqrt(2x) - 3 = 4

sqrt(2 * 24.5) - 3 = 4

sqrt(49) - 3 = 4

7 - 3 = 4

4 = 4, OK→ x = 24.5 is a VALID SOLUTION




If the equation is: sqrt(2x - 3) = 4


x = 9.5

replace every x in the equation with 9.5

sqrt(2x - 3) = 4

sqrt(2 * 9.5 - 3) = 4

sqrt(16) = 4

4 = 4, OK→ x = 9.5 is a VALID SOLUTION








Thanks for writing.

Staff
www.solving-math-problems.com


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