Question

Solve: 3 + 4(7-h) - 4(3h-1) = 0

Answer 1

Hint: In case of such a linear equation open all the brackets one by one and keep simplifying the terms with the given addition or subtraction option until we are down to a constant and a variable with some coefficient.
Complete step-by-step answer:
A linear equation in one variable is an equation of a straight line, written in one variable. The highest power of the variable is 1. Linear equations in one variable may take the form ax + b = 0 and are solved using basic algebraic operations.
What we have here is a conditional equation. A conditional equation is true for only some values of the variable. For example, if we are to solve the 5x+2=3x−6, we have the following:
5x+2=3x−6,
$\Rightarrow$ 2x=−8,
$\Rightarrow$ x=−4
The solution set consists of one number: {−4}. It is the only solution.
On a general note about linear equation in one variable we can say that:
A linear equation in one variable can be written in the form ax+b=0
where a and b are real numbers, a≠0.
Now we have the Equation 3 + 4(7-h) – 4(3h-1) = 0,
Opening all the brackets we get 3 + 28 - 4h – 12h + 4 = 0,
$\Rightarrow$ 35 – 16h = 0,
$\Rightarrow$ 35 = 16h,
$\Rightarrow$ h=$\dfrac{35}{16}$
$\Rightarrow$ h = 2.1875.
So, the value of h = 2.1875.

Note: We can add or subtract the same quantities on either side of an equation so to make sure there is no error bring all variables on one side and constants on the other. Also, to check if you have got the correct value put the value back in the original equation and we should obtain L.H.S. = R.H.S.