Solve for x
Solve for x is all related to finding the value of x in an equation of one variable that is x or with different variables like finding x in terms of y. When we find the value of x and substitute it in the equation, we should get L.H.S = R.H.S.
1.  What Does Solve for x Mean? 
2.  How Do You Solve for x? 
3.  Solve for x in The Triangle 
4.  Solve for x in Fractions 
5.  Solve for x Equations 
6.  FAQs on Solve for x 
What Does Solve for x Mean?
Solve for x means finding the value of x for which the equation holds true. i.e when we find the value of x and substitute in the equation, we should get L.H.S = R.H.S
If I ask you to solve the equation 'x + 1 = 2' that would mean finding some value for x that satisfies the equation.
Do you think x = 1 is the solution to this equation? Substitute it in the equation and see.
1 + 1 = 2
2 = 2
L.H.S = R.H.S
That’s what solving for x is all about.
How Do You Solve for x?
To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.
Let’s start with a simple equation as, x + 2 = 7
How do you get x by itself?
Subtract 2 from both sides
⇒ x + 2  2 = 7  2
⇒ x = 5
Now, check the answer, x = 5 by substituting it back into the equation. We get 5 + 2= 7.
L.H.S = R.H.S
Solve for x in the Triangle
Solve for x" the unknown side or angle in atriangle we can use properties of triangle or thePythagorean theorem.
Let us understand solve for x in a triangle with the help of an example.
△ ABC is rightangled at B with two of its legs measuring 7 units and 24 units. Find the hypotenuse x.
In △ABC by using the Pythagorean theorem,
we get AC^{2} = AB^{2} + BC^{2}
⇒ x^{2 }= 7^{2 }+ 24^{2 }
⇒ x^{2 }= 49 + 576
⇒ x^{2} = 625
⇒ x = √625
⇒ x = 25 units
Solve for x to find Missing Angle of Triangle
Suppose angle A = 50°, angle B = 60°, and angle C = x are the angles of a triangle. ABC. By using the angle sum property we can find the value of x.
angle A + angle B + angle C = 180 degrees.
50° + 60° + x° = 180° ⇒ x = 70°
Solve for x in Fractions
Solve for x in fractions, we simply do the cross multiplication and simplify the equation to find x.
For example: Solve for x for equation ⇒ 2/5 = x/10.
Cross multiply the fractions
⇒ 2 × 10 = 5 × x
Solve the equation for x
⇒ x = 20 / 5
Simplify for x
⇒ x = 4
To verify the x value put the result, 4 back into the given equation
⇒ 2/5 = 4/10
Cross multiply the fractions
⇒ 2 × 10 = 4 × 5
⇒ 20 = 20
L.H.S = R.H.S
Solve for x Equations
We can use a system of equations solver to find the value of x when we have equations with different variables.
We solve one of the equations for the x variable (solve for x in terms of y) and then substitute it in the second equation, and then solve for the y variable.
Finally, we substitute the value of the x variable that we found in one of the equations and solve for the other variable.
Let us understand solve for x and y with the help of an example.
For example, Solve for x: 2x  y = 5, 3x + 2y = 11
⇒ 2x  y = 5
Adding y on both sides we get,
⇒ 2x  y + y = 5 + y
⇒ 2x = 5 + y
⇒ x = (5 + y) / 2
Above equation is known as x in terms of y.
Substitute x = (5 + y) / 2 in second equation 3(5 + y) / 2 + 2y = 11
⇒ (15 + 3y) / 2 + 2y = 11
⇒ (15 + 3y + 4y) / 2 = 11
⇒ (15 + 7y) / 2 = 11
⇒15 +7y = 22
⇒ 7y = 22  15
⇒ 7y = 7
⇒ y=1
Now, substitute y = 1 in x = (5+y) / 2
⇒ x = (5 + 1) / 2
⇒ 6 / 2 = 3
Thus, the solution of the given system of equations is x = 3 and y = 1.
Important Notes on Solve for x
 To solve for x (the unknown variable in the equation), apply arithmetic operations to isolate the variable.
 For solving 'x' number of equations we need exactly 'x' number of variables.
 Solve for x and y can be done by the substitution method, elimination method, crossmultiplication method, etc.
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Solve for x Examples

Example1: Solve for x: 2 ( 3x + 1 ) + 3 ( 5x + 2 ) = x  1
Solution: 2 (3x + 1) + 3 (5x + 2) = x  1
⇒ 6x + 2 + 15x + 6 = x  1
⇒ 8 + 21x = x  1
⇒ 20x = 9
⇒ x = 9/20

Example 2: It is given that x is the one side of the chessboard and it is smaller than its perimeter by 18 inches. Form an equation and solve for x?
Solution: The side of chessboard = 'x' inches
Since the chessboard is square (all sides are equal), therefore its perimeter will be '4x' inches
According to the given condition,
Perimeter = x + 18
⇒ 4x = x + 18
⇒ 4x  x = 18
⇒ 3x = 18
⇒ x = 18/3
⇒ x = 6
The side of the chessboard is 6 inches.

Example 3: The ages of Roony and Herald are 5x and 7x. If four years later, the sum of their ages will be 56 years, then form an equation and solve for x.
Solution: The Rooney and Herald's age is 5x and 7x.
The sum of their ages after 4 years = 56
According to given condition,
⇒ (5x+4) + (7x+4) = 56
⇒ 5x + 7x + 4 + 4 = 56
⇒ 12x + 8 = 56
⇒ 12x = 56  8
⇒ 12x = 48
⇒ x = 48/12
⇒ x = 4
The age of Roony = 5 × 4 = 20 years
The age of Herald = 7× 4 = 28 years
FAQs on Solve For x
How Do You Solve for x in a Bracket?
To solve for x in a bracket we use distributive law and remove the bracket, move all the x terms to one side and constant to the other side and find the unknown x.
For example, 2(x−3) = 4
By using distributive law, 2x  6 = 4 ⇒ 2x = 4 + 6 ⇒ 2x = 10 ⇒ x = 10/2 ⇒ x = 5
How Do You Solve for x in a Fraction?
To solve for x in fractions we have to eliminate the denominator by cross multiplication and then solve for x.
For example, x/4 + 1/2 = 5/2 ⇒ (2x+4)/8 = 5/2
By doing cross multiplication we get, 2(2x + 4) = 8(5)
⇒ 4x + 8 = 40
⇒ 4x = 40  8
⇒ 4x = 32
⇒ x = 32 / 4
⇒ x = 8
How Do You Solve for x for the Equation 4x + 2 = 8?
To solve for x follow the points.
 Start with 4x + 2 = 8
 Subtract 2 from both sides: 4x = 8  2 = 10
 Divide by 4: x = 10 ÷ 4 = 5/2
 x = 5/2
How Do You Solve for x for the Equation 3x  7 = 26?
To solve for x follow the points.
 Start with 3x  7 = 26
 Add 7 to both sides: 3x  7 + 7 = 26 + 7
 Calculate: 3x = 33
 Divide by 3: x = 33 ÷ 3
 x = 11
How Do You Solve for x in Vertical Angles?
Vertical angles are congruent, or we can say they have same measure. For example, if a vertical angle equals 2x and the other equals 90  x, we would simply form an equation 2x = 90  x.
2x = 90  x
Add x to both sides, 2x + x = 90 x + x
3x = 90
x = 30
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