Question

How do you solve `78> 4x + 6`?

Answer 1

See a solution process belowL

Explanation:

First, subtract `color(red)(6)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`78 - color(red)(6) > 4x + 6 - color(red)(6)`

`72 > 4x + 0`

`72 > 4x`

Now, divide each side of the inequality by `color(red)(4)` to solve for `x` while keeping the inequality balanced:

`72/color(red)(4) > (4x)/color(red)(4)`

`18 > (color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4))`

`18 > x`

We can reverse or "flip" the entire inequality to state the solution in terms of `x`:

`x < 18`

Answer 2

`x<18`

Explanation:

For now, we can treat the inequality sign like an equal sign. We perform the normal operations as if this were `78=4x+6`.

We start by subtracting `6` from both sides to get:

`72>4x`

We can switch the sides if we like:

`4x<72`

And we can divide both sides by `4` to get:

`x<18` or `18>x`

*NOTE: The direction of the inequality does not change since I did not multiply or divide it by a negative. I only flipped the sign because the convention is usually to have the variable on the left.