Verified answer

Maybe a detailed explanation will help you.

-5 < x + 1

We want to isolate the numbers on one side of the < sign and the variables on the other side. To do that for this equation, we must subtract 1 from both sides of the < sign

-5 - 1 < x + 1 - 1

-6 < x + 0

-6 < x

we can flip this equation around to make it clearer

x > -6

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By itself, x^2 - 5x can't be solved because there is no relationship sign such as "=" or "<" or ">". However, if we make an assumption, then it can be solved.

So I will assume that

x^2 - 5x = 0

I like using the perfect square method. That is where we add a number (A) to both sides to make the variable side a perfect square so that it can be factored.

To do this, we need to use the -5 from the -5x term. We first take 1/2 of -5 (=-2.5), and then square it (=6.25). This gives us the value for A.

x^2 - 5x + A = 0 + A

x^2 - 5x + 6.25 = 0 + 6.25

x^2 - 5x + 6.25 = 6.25

Notice that we have a perfect square on the left side of the = sign. So we need to factor it.

(x - 2.5)(x - 2.5) = 6.25

(x - 2.5)^2 = 6.25

Next we take the square root of both sides.

√(x - 2.5)^2 = √6.25

x - 2.5 = 2.5

We need to solve for x by isolating the variable on one side of the = sign and the numbers on the other side. To do that here, we just add 2.5 to both sides.

x - 2.5 + 2.5 = 2.5 + 2.5

x = 5.0

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Once again, since we don't have a relationship sign such as "=", "<" or ">", we can't solve for x. But we can simplify this equation.

This equation has three terms. Unfortunately, I'm not positive if the y is under the radical sign.

If I assume that the y is under the radical sign for each term, then the solution is as follows.

5√(2y) + 3√(32y) - 2√(27y^2)

The first term 5√(2y) cannot be simplifed any further.

The second term 3√(32y) can be simplifed because the 32 can be factored using numbers other than 32 and 1.

Since we can't simplify the first term, we must try to simplify the other terms so that they match the radical for the first term if that is possible. So we have to factor out something from √32y to end up with √2y.

Notice that 32 is 16 times 2 and 16 is a perfect square. So

3 * √(32 * y)

3 * √(16 * 2 * y)

3 * (√16) * √(2y)

3 * (4) * √(2y)

12√(2y)

The third term 2√(27y^2) can be simplified. Let us just deal with the square root part first.

√(27 * y^2)

√27 * √y^2

We need only a 2 under the square root sign. Unforatunately, we can't factor 27 into a perfect square times 2. But we can factor the 27 into 9 * 3 since 9 is a perfect square.

√(9 * 3) * √y^2

√9 * √3 * √y^2

3 * √3 * √y^2

Also notice that the square root of a number that is squared is just that number. So, √y^2 = y

The third term simplifies to

3 * √3 * y

3y√3

Combining all three terms, we have

5√(2y) + 12√(2y) - 3y√3

Since the first two terms have the same radicals, we can perform the addition between them.

17√(2y) - 3y√3

this is the final answer.

1.) x=-5

2.) x= 0 or -5

3.) (5*2y^1/2)+(3*32y^1/2)-(2*27y^1/2)

=9.3y+29.4y-11.8y

=26.9y