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How do you solve for x in $4.2(3.1 + 6.4x) = 17.5x \pm 2.3$ ?

Last updated date: 29th Feb 2024
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Hint:In this question, we are given an expression containing one unknown variable quantity (x) so it is known as an algebraic expression. We know that we need an “n” number of equations to find the value of “n” unknown variables. We have exactly one equation and 1 unknown quantity, so we can easily find the value of x by rearranging the equation such that one side of the equation contains the terms containing x and all other terms lie on the other side. Then by applying the given arithmetic operations, we can find the value of x.

We are given that $4.2(3.1 + 6.4x) = 17.5x \pm 2.3$
We will first simplify the terms on the left-hand side –
$13.02 + 26.88x = 17.5x \pm 2.3$
Now the above expression is a combination of two expressions, so we can split it into two
expressions as –
$13.02 + 26.88x = 17.5x + 2.3$ and $13.02 + 26.88x = 17.5x - 2.3$
To find the value of x, we will rearrange the equations as follows –
$26.88x - 17.5x = 2.3 - 13.02$ and $26.88x - 17.5x = - 2.3 - 13.02$
$\Rightarrow 9.38x = - 10.72$ and $9.38x = - 15.32$
$\Rightarrow x \approx - 1.143$ and $x \approx - 1.633$
Hence, when $4.2(3.1 + 6.4x) = 17.5x \pm 2.3$ , we get $x = - 1.143$ and $x = - 1.633$

Note: In the given algebraic expression, the alphabet representing the unknown quantity has a non-negative integer as power, that is, 1. So the given expression is a polynomial equation and degree is defined as the highest power of the unknown quantity in a polynomial equation, so the given equation is a linear equation as the degree of x is 1. We know that a polynomial equation has as many solutions as the degree of the equation, so the given equation should have exactly one solution but it is a combination of two equations that’s why we get 2 values of x.