What Is X In Algebra

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There are a number of ways to solve for 10, whether you're working with exponents and radicals or if you simply have to do some division or multiplication. No matter what process yous use, you always accept to find a way to isolate ten on i side of the equation so you can discover its value. Here's how to practise it:

1
Write downwards the problem. Here information technology is:
- 2^two(ten+3) + 9 - 5 = 32
2
Resolve the exponent. Remember the society of operations: PEMDAS, which stands for Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction.^[1] You tin't resolve the parentheses first considering ten is in the parentheses, so you should kickoff with the exponent, 2^two. 2² = four
- iv(x+3) + 9 - 5 = 32
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3
Do the multiplication. ^[2] Just distribute the 4 into (ten +iii). Here's how:
- 4x + 12 + 9 - 5 = 32
4
Do the improver and subtraction. Just add or subtract the remaining numbers. Here's how:
- 4x+21-five = 32
- 4x+16 = 32
- 4x + sixteen - 16 = 32 - xvi
- 4x = 16
v
Isolate the variable. ^[3] To do this, but divide both sides of the equation past 4 to observe 10. 4x/4 = ten and 16/4 = 4, so x = 4.
- 4x/4 = xvi/iv
- x = 4
6
Check your work. ^[4] Just plug x = 4 dorsum into the original equation to brand sure that information technology checks out. Here's how:
- two²(ten+3)+ 9 - five = 32
- 2²(4+3)+ 9 - 5 = 32
- 2²(7) + 9 - 5 = 32
- 4(7) + 9 - v = 32
- 28 + ix - five = 32
- 37 - 5 = 32
- 32 = 32

one
Write down the trouble. Let's say you lot're working with this problem where the x term includes an exponent:
- 2x² + 12 = 44
2
Isolate the term with the exponent. ^[5] The get-go thing you should exercise is combine like terms then that all of the constant terms are on the correct side of the equation while the term with the exponent is on the left side. Just subtract 12 from both sides. Here's how:
- 2x²+12-12 = 44-12
- 2x^two = 32
iii
Isolate the variable with the exponent past dividing both sides by the coefficient of the x term. In this case, ii is the x coefficient, so divide both sides of the equation past 2 to go rid of it. Hither's how:
- (2x²)/two = 32/2
- xⁱⁱ = sixteen
4

Take the foursquare root of each side of the equation. ^[6] Taking the square root of x² volition cancel it out. So, take the square root of both sides. You lot'll get x left over on one side and plus or minus the square root of 16, 4, on the other side. Therefore, x = ±four.
5
Bank check your piece of work. Only plug 10 = 4 and x = -4 back in to the original equation to make sure information technology checks out. For example, when you're checking x=4:
- 2x² + 12 = 44
- ii x (4)² + 12 = 44
- ii 10 xvi + 12 = 44
- 32 + 12 = 44
- 44 = 44

1
Write down the trouble. Let's say you lot're working with the post-obit problem:^[vii]
- (x + 3)/6 = 2/iii
2
Cross multiply . To cross multiply, simply multiply the denominator of each fraction by the numerator of the other fraction.^[8] You lot'll exist essentially multiplying in two diagonal lines. Then, multiply the first denominator, 6, past the 2nd numerator, 2, to become 12 on the right side of the equation. Multiply the 2nd denominator, three, by the first numerator, 10 + 3, to get three 10 + 9 on the left side of the equation. Here's how it will look:
- (x + three)/six = 2/3
- 6 x ii = 12
- (x + 3) ten 3 = 3x + 9
- 3x + 9 = 12
3
Combine like terms. Combine the constant terms in the equation to subtract 9 from both sides of the equation.^[9] Here'southward what you do:
- 3x + 9 - nine = 12 - ix
- 3x = 3
4

Isolate ten by dividing each term past the 10 coefficient. Just divide 3x and 9 past iii, the x term coefficient, to solve for 10. 3x/3 = x and 3/iii = 1, then yous're left with x = 1.^[10]
5
Cheque your piece of work. To check your work, just plug x back in to the original equation to make certain that it works.^[eleven] Here'southward what you exercise:
- (x + iii)/6 = 2/3
- (1 + iii)/half dozen = two/iii
- 4/vi = two/iii
- 2/iii = ii/3

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ane
Write downward the problem. Let's say you're solving for 10 in the following trouble:^[12]
- √(2x+9) - 5 = 0
2
Isolate the square root. You have to motility the part of the equation with the square root sign to one side of the equation before you can proceed. And then, you lot'll have to add five to both sides of the equation. Here's how:
- √(2x+9) - 5 + v = 0 + 5
- √(2x+nine) = 5
3
Square both sides. Only equally you would dissever both sides of an equation by a coefficient that is being multiplied by x, you lot would square both sides of an equation if ten appears under the square root, or the radical sign. This will remove the radical sign from the equation. Here'southward how you do it:
- (√(2x+9))² = vⁱⁱ
- 2x + 9 = 25
4
Combine similar terms. Combine like terms by subtracting both sides past 9 then that all of the constant terms are on the right side of the equation while 10 remains on the left side. Here's what you practice:
- 2x + 9 - ix = 25 - 9
- 2x = 16
5

Isolate the variable. The last thing y'all have to do to solve for ten is to isolate the variable by dividing both sides of the equation by 2, the coefficient of the x term. 2x/ii = ten and 16/2 = 8, so y'all're left with x = eight.
six
Check your work. Plug 8 back in to the equation for 10 to come across if you become the correct reply:
- √(2x+9) - five = 0
- √(2(eight)+ix) - 5 = 0
- √(sixteen+nine) - 5 = 0
- √(25) - 5 = 0
- 5 - 5 = 0

1
Write downward the problem. Let's say you lot're trying to solve for x in the following problem:^[xiii]
- |4x +2| - vi = 8
2
Isolate the accented value. The get-go thing you take to do is to combine like terms and become the terms inside the absolute value sign on one side. In this case, you would practise it past calculation 6 to both sides of the equation. Here'southward how:
- |4x +two| - 6 = 8
- |4x +ii| - 6 + half dozen = 8 + 6
- |4x +2| = fourteen
3
Remove the accented value and solve the equation. This is the kickoff and easiest step. Yous'll have to solve for x twice whenever you work with absolute value. Here'south how you do it the kickoff time:
- 4x + 2 = xiv
- 4x + 2 - ii = 14 -ii
- 4x = 12
- x = three
four
Remove the accented value and change the sign of the terms on the reverse side of the equal sign before yous solve. Now, practice it once again, except set the first part of the equation equal to -14 instead of xiv. Here's how:
- 4x + 2 = -14
- 4x + 2 - 2 = -fourteen - 2
- 4x = -16
- 4x/4 = -16/4
- ten = -four
5
Check your work. At present that you lot know that x = (3, -4), just plug both numbers dorsum in to the equation to see that information technology works. Here's how:
- (For ten = 3):
  - |4x +ii| - 6 = eight
  - |four(3) +two| - 6 = viii
  - |12 +2| - 6 = 8
  - |xiv| - half dozen = 8
  - fourteen - 6 = 8
  - viii = viii
- (For ten = -four):
  - |4x +ii| - 6 = 8
  - |iv(-4) +2| - 6 = viii
  - |-16 +two| - six = 8
  - |-fourteen| - half dozen = 8
  - 14 - 6 = 8
  - 8 = eight

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What is the beginning step in solving for Ten?

David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over x years of teaching experience, David works with students of all ages and grades in diverse subjects, also as college admissions counseling and examination preparation for the SAT, Human action, ISEE, and more. After attaining a perfect 800 math score and a 690 English language score on the Saturday, David was awarded the Dickinson Scholarship from the Academy of Miami, where he graduated with a Available's degree in Business Administration. Additionally, David has worked as an teacher for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

Get-go on the side of the equation with X and do the inverse operations to isolate X. For example, if the equation was X + 5 = x, yous would decrease 5 from each side.
Question

How I solve this problem: 15 : 1000 : ten : 100?

If the problem is xv:i,000 = x:100, re-write it as i fraction equal to another: 15 / 1,000 = x / 100. Solve for x either by inspection or by cross-multiplication.
Question

Solve for x; Peter is twice as onetime as his son. Twelve years ago he was four times older than him. How old are they at present?

Allow x be the son's current age. And then 2x is Peter'south current age. Twelve years ago the son'southward age was (x-12), and Peter's historic period was (2x-12). Ready an equation stating that Peter's age 12 years ago was 4 times the son'south age then. Solve for x and 2x.

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To check your work, plug the value of x back into the original equation and solve.

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Radicals, or roots, are some other way of representing exponents. The square root of ten = 10^1/2.

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Article Summary Ten

To solve for x in a basic linear equation, start by resolving the exponent using the guild of operations. And then, isolate the variable to go your answer. To solve for x when the equation includes an exponent, start by isolating the term with the exponent. Then, isolate the variable with the exponent past dividing both sides by the coefficient of the 10 term to get your reply. If the equation has fractions, first by cross-multiplying the fractions. Then, combine like terms and isolate x by dividing each term by the 10 coefficient. If you desire to larn how to solve for ten if the equation has radicals or absolute values, go on reading the article!

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