Question

Which of the following is NOT a solution to -4x + 9 > -3

A: -3
B: -1
C: 3
D:5

Answer 1

D

Explanation:

-4x + 9 ≥ -3 Subtract 9 from both sides

-4x ≥ -12 Divide both sides by -4. When you divide both sides by a negative number, you must flip the inequality sign.

x ≤ 3

D: 5 is not a solution.

Answer 2

D) 5

Explanation:

To solve this problem, we must first isolate the variable and simplify the inequality. Isolating the variable means having the variable on one side of an equation or inequality without any other terms?

How do you isolate a variable?

Here's an example.

x+3=18

What can we do to have x on its own side of the equation? Currently, 3 is also with it. If we subtract 3 on both sides, we are leaving the equation with the same answer.

x + 3 - 3= 18 - 3

Combine like terms.

x = 21

That's how you solve for an equation.

Next, an example with division.

3x = 21

How do we solve for x this? Well, we know that 3x = 3 times x. So, to solve for x, we remove the 3. Since its 3 times x, lets divide by 3 on both sides.

`(3x)/(3) =\frac{21} {3}`

Simplify:

3x/3 means 3 times x divided by 3. 3/3 = 1

1x = 21/3

21/3 = 7

x = 7

Now lets get to the problem.

`-4x + 9 \geq -3`

The first step is to subtract by 9 on both sides so we can work our way to isolating the variable and solving the problem.

`-4x + 9 -9\geq -3 - 9`

Simplify.

`-4x \geq -12`
`-4x \geq -12`

Now heres the tricky part. To solve for an equation, we must remove -4 from x, or -4 times x. In an equality, which states that:

A
`\geq , \leq , > , or < B`

If you divide or multiply both sides by a negative number, which means the number is less than 0, you must flip the sign!

When you multiply/divide by a negative number or both sides in an equality:

`\leq`
`\geq`

`\geq`
`\leq`

> <

< >

So, we currently have:

`-4x \geq -12`

Divide by -4 on both sides.

`(-4x)/(-4) \geq (-12)/(-4)`

Simplify. (Use the rule which states that a negative number multiplied or divided by another negative number equates to a positive number).

`x \geq 3`

Flip the sign (This is a crucial step!)

`x \leq 3`

Now,
`x \leq 3` means any number equal to or lower than 3 satisfies the conditions of the inequality.

Is -3 lower than or equal to 3?

Yes; Lower

Is -1 lower than or equal to 3?

Yes;

Is 3 lower than or equal to 3?

Yes; Equal

Is 5 lower than or equal to 3?

No; Greater

D, 5 is your answer as it does not satisfy the inequality.