Question

Solve the inequality 2x < 8 - 4(2 - x)

Answer 1

how would you solve say the EQUALITY of -> 2x = 8 - 4(2 - x) ?

Answer 2

well i would distribute the -4

Answer 3

right, so... what would you end up with?

Answer 4

well i tried solving it myself and i got 4 but my teachersaid it was wrong so then i got 2

Answer 5

First, let's work on the left hand side of your inequality, the 2x
This means, for instance, to see if it can be simplified at all.
Multiply x and 2
Multiply x and 1


The x just gets copied along.

The answer is x

x

2*x evaluates to 2x

So, all-in-all, the left hand side of your inequality can be written as: 2x

Now, let's work on the right hand side of your inequality, the 8 - 4(2 - x)
2-x evaluates to 2-x
Multiply 4 by 2-x

we multiply 4 by each term in 2-x term by term.

This is the distributive property of multiplication.

Multiply 4 and 2


1

4 × 2 = 8

Multiply 4 and -x

Multiply 1 and x


The x just gets copied along.

x

4 × -x = -4x

4*(2-x) evaluates to 8-4x

8 - 8 = 0

The answer is 4x

8-4*(2-x) evaluates to 4x

The right hand side of your inequality can be written as: 4x

So with these (any) simplifications, the inequality we'll set out to solve is:
2x ‹ 4x

Move the 4x to the left hand side by subtracting 4x from both sides, like this:
From the left hand side:
2x - 4x = -2x

The answer is -2x

From the right hand side:
4x - 4x = 0

The answer is 0


Now, the inequality reads:
-2x ‹ 0
To isolate the x, we have to divide both sides of the inequality by the other "stuff" (variables or coefficients)
around the x on the left side of the inequality.

The last step is to divide both sides of the inequality by -2 like this:
To divide x by 1


The x just gets copied along in the numerator.

The answer is x

-2x ÷ -2 = x


0 ÷ -2 = 0


Note! Here's an important point about inequalities:
We are now dividing by -2, which is a number less than zero! This changes the form of your inequality. Or, in other words, your ‹ will now become a ›.

The solution to your inequality is:
x › 0
So, your solution is:
x must be greater than 0

Answer 6

thank you so much