Solve for x for each literal equation?

Question

what is a literal equation??????


1) 1/2ax=c
2) p+x=q
3) rx=8=e
4)dx+ax=2a

Answer 1

1) x = 2c/a
2) x = q - p
3) x = 8/r (or is that "8 - e" instead of "="?)
4) x = 2a/(d + a)

Details:

1/2 ax = c

Multiply both sides by two:

2 * 1/2 ax = 2 * c
ax = 2c

Divide both sides by a

ax/a = 2c/a
x = 2c/a

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p + x = q

Subtract p from both sides

p + x - p = q - p
x = q - p

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rx = 8 = e

If that's actually two equals signs, you can ignore the e one, and just divide by r:

rx/r = 8/r
x = 8/r

If it's supposed to be rx - 8 = e, then first add 8 to both sides:

rx - 8 + 8 = e + 8
rx = e + 8

Then divide by r

rx/r = (e + 8)/r
x = (e + 8)/r

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dx + ax = 2a

First use distributive to factor out x:

x(d + a) = 2a

Then divide both sides by (d + a):

x(d + a)/(d + a) = 2a/(d + a)
x = 2a/(d + a)

Answer 2

To move things to the other side of the equal sign, just do their opposite calculation: add - subtract, divide - multiply.

1) 1/2ax=c
x = c / (1/2a) <-- just divide each side by this since it's multiplied on the other side.
x = 2c/a

2) p+x=q
x = q - p <--just subtract p since it's added on the other side.

3) rx=8=e <-- two equal signs?
rx = 8 - e
x = (8 - e) / r <-- divide by r, since it's multplied on the other side.

4)dx+ax=2a
x(d+a) = 2a <-- factor out "x" first.
x = 2a / (d+a) <--once again, just divide (opposite from the other side - multiplied).

Literal equation (Math.), an equation in which known quantities are expressed either wholly or in part by means
of letters; -- distinguished from a numerical equation.

Answer 3

This means there is no numerical answer since you are given no numbers. You have to solve for all these in terms of x, with the other variables still in the answer.

1) x= 2c / a
2) x= q- p
3) x= 8 / r or e / r
4) x= 2a / d+a

Answer 4

1. x= 2c/a
2. x=q-p
3. x= 8/r did you mean rx=8-e that would be x = (8-e)/r
4. x= 2a / (d+a)

Not sure if literal equation means just play along and work with it!

Answer 5

2x + 3y = 6 to remedy for x, placed it via itself --- subtract 3y 2x = -3y + 6 --- divide via 2 to get x on my own x = -3/2y + 3 --- the 6 is split via 2 so it equals 3. -3/2y is in lowest type already. =)