The possible value of x is 3. So option 3 is the correct answer.
What is a linear equation?
"A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form ax + b = 0".
For the given situation,
The linear equation is given as [tex](4x-5)^2=49[/tex]
Taking square root on both sides,
⇒ [tex]4x- 5=\sqrt{49}[/tex]
⇒ [tex]4x-5=7[/tex]
Substitute, [tex]x=-\frac{4}{5}[/tex]
⇒[tex]4(\frac{-4}{5} )-5=7[/tex]
⇒[tex]\frac{-41}{5} = 7[/tex]
This is not equal. So x does not satisfy -4/5.
Substitute, [tex]x=\frac{-1}{2}[/tex]
⇒ [tex]4(\frac{-1}{2} )-5=7[/tex]
⇒ [tex]-7=7[/tex]
This is not equal. So x does not satisfy -1/2.
Substitute, [tex]x=3[/tex]
⇒ [tex]4(3)-5=7[/tex]
⇒ [tex]7=7[/tex]
This is equal. So x satisfies 3.
Substitute, [tex]x=5[/tex]
⇒ [tex]4(5)-5=7[/tex]
⇒ [tex]15=7[/tex]
This is not equal. So x does satisfy 5.
Substitute, [tex]x=7[/tex]
⇒ [tex]4(7)-5=7[/tex]
⇒ [tex]23=7[/tex]
This is not equal. So x does not satisfy 7.
Hence we can conclude that the possible value of x is 3. So option 3 is the correct answer.
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