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Last updated date: 20th Jun 2024
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Answer
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Hint: In the given problem $4x-2<10$ write $'='$ equal to one the place of $'<'$ less than symbol.
Then solve the modified equation. Add $'2'$ on both sides i.e. left side and right side. And now divide both sides by $'4'$ and at least replace $'='$ equal sign by less than $'<'$ sign.

Complete step by step solution:As per the given question,
$x-2<10$ given equation. Write $'='$ equal to one the place of $'<'$ less than symbol. Therefore the modified equation will be this form.
$4x-2=10$
Add $'2'$ on both sides i.e. left side and right side.
$4x-2+2=10+2$
Here, on the left side $'-2'$ and $'+2'$ will get canceled.
$\therefore 4x=12$
$'4'$ which is in multiplication with $'x'$ shift to right side and the multiplication get converted into division.
$x=\dfrac{12}{4}$
As you divide $12$ by $4.$
The value of $x$ will be, as $4\times 3=12$
$x=3...(i)$
Again replace $'='$ sign by $'<'$ less than sign, in equation $(i)$
$\therefore x<3$
In this way you can solve $4x-2<10$

Additional Information:
Linear equation: An equation for a straight line is called a linear equation. The general representation of the straight line equation is $y=mx+b,$ where $m$ is slope of line and $b$ is the $y$-intercept. Linear equations are those equations that are of the first order. These equations are defined for lines in the coordinate system. The number $'m'$ and $'b'$ give the slope of the line $(m)$ and the value of $y$ when $x$ is $0(b).$ The value of $y$-intercept because $\left( 0,y \right)$ is the point at which the line crosses the $y$-axis.

Note:
Replace $'<'$ by $'='$ equal to sign in the given linear equation. Five forms of linear equation:
(1) General form
(2) Slope intercept form
(3) Point form
(4) Intercept form
(5) Two point form.