‘X’ is used in algebra as a variable. It is often used for unknown values.
‘X’ is sometimes called ‘unknown’.
Variables can be letters, numbers, symbols, or a combination of those. It does not have to be “X”. It can be either “Y” or “W”.
For example:
x+1=5
x =5-1
x =4
Here x is unknown and the value for x is 4.
How Do You Solve for x?
Solve the equation for x by putting the variable on one side and putting all the remaining values on the other side. Calculate the result by simplifying the values.
Let’s solve the equation as
x + 5= 9
Subtract 2 from both sides
⇒ x + 5- 5 = 9 – 5
⇒ x = 4
Now, check the answer, x = 4 by back substitution in the equation. We get 4 + 5= 9.
L.H.S = R.H.S
To find an unknown angle in a triangle
Using properties of triangles or the Pythagorean theorem, we can solve for x the unknown side or angle in a triangle.
Let’s
solve for x in a triangle
△ ABC is right-angled at B with two of its legs measuring 3 units and 4 units. Find the hypotenuse x.
[katex]{(x)}^2={(4)}^2+{(3)}^2[/katex].
[katex]x^2=16+9[/katex].
[katex]x^2=25[/katex].
[katex]x=5[/katex].
Solve for Equations
We solve two equations for x,
[katex]x-4y=4 [/katex] [katex] eq(1)[/katex].
[katex]4x-y=16[/katex] [katex]eq(2)[/katex].
From eq(1)
Derive the value of x
[katex]x=4+4y[/katex] [katex]eq(3)[/katex].
Put it [katex]x=4+4y[/katex]. in eq(2)
[katex]4(4+4y)-y[/katex] =[katex]16[/katex].
[katex]16+16y-y[/katex] =[katex]16[/katex].
[katex]15y[/katex] = [katex]16-16[/katex].
[katex]y=0[/katex].
Put [katex]y=0[/katex] [katex]eq(3)[/katex].
[katex]x=4+4y[/katex].
[katex]x=4+4(0)[/katex].
[katex]x=4[/katex].
[katex][x,y] =[4,0][/katex].
Solve for x in Fractions
we simply do the cross multiplication and simplify the equation to find x.
[katex]\frac x{20}=\frac3{10}[/katex].
Multiply both sides with [katex]20[/katex].
[katex]\frac x{20}\times20=\frac3{10}\times20[/katex].
[katex]x=2\times2[/katex].
[katex]x=4[/katex].