Mathematics: How exactly do i rewrite the equation for x, and express its value in terms of a? i m still confused after the lesson, and would really appreciate if anybody could me. 3 x - 4 = 20 a

How exactly do i rewrite the equation for x, and

Ответ:

momo1039

12.03.2022

What "in terms of" means

Okay! When they say "put x in terms of a," what they're essentially asking is "get the equation in a form that tells us exactly what we have to do to a in order to get x."

For a quick example, say we're given the equation x - y = 1, and we want to put x in terms of y. If we add y to either side of the equation, we get the equation x = y + 1. This tells us that, if we start at y, we just add 1 to it, and that gets us to x. We can clearly see how to get from y to x, so we say that x is in terms of y.

An equivalent way of phrasing the process is that we want to solve the equation for the variable we're putting in terms of another. In this example, that variable is x.

The actual problem

Onto the problem we have here, we're given the equation

$\frac{3}{a}x-4=20$

and we want to put x in terms of a. We want to make this equation tell us exactly what we need to do in order to turn a into x, which means we need to get the x and the a onto opposite sides of the equation. Here are the steps to make that happen:

Add 4 to either side to get rid of the -4 on the left side:

$\frac{3}{a} x-4+4=20+4\\\\\frac{3}{a}x=24$

Multiply either side by a to cancel the a in the denominator on the left side:

$a\big(\frac{3}{a}x\big)=24a\\3x=24a$

Divide either side by 3 to cancel the 3 in 3x:

$(3x)/3=(24a)/3\\x=8a$

This tells us that, in order to get x from a, we simply have to multiply a by 8. This is exactly the form we were looking for, so x is described in terms of a by the formula x = 8a.