Twice the difference of a number + -3 is 4 find the number

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

7 0

Answer:

The number is 5

Step-by-step explanation:

If we need to find the hidden number, Which for simplicity's sake we will denote as "n", lets first write out the equation.

"2 x [n + (-3)] = 4"

We can work through this problem backwards. if we need two times the sum of "n" and (-3) to get to 4, the only number that can be multiplied by 2 to get a product of 4 is 2, so "n" + (-3) must equal 2. so, From here, we can figure out that since 5 + (-3) equals 2, "n" Must equal 5. so, if we plug in 5 for "n" the equation looks like this:

"2 x [5 + (-3)] = 4"

So, since the equation makes sense, the answer is, "n = 5"

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What is the factored form of 2x2 + x-3?

Vesnalui [34]

Answer:

Step-by-step explanation:

a = 2, b = 1, c = -3

We need to factor this by finding the product of a and c, then from there find which factors of a * c will either add or subtract to give us b.

a * c = 6 and the factors of 6 and 1 and 6, 2 and 3. Well, 6 - 1 doesn't equal 1 and neither does 6 + 1. So our factors are 3 and 2. In order to combine those to get a 1 (our b), we will subtract 2 from 3 since 3 - 2 = 1. That means that 3 is positive and 2 is negative. Filling in the formula with 3 and 2 in place of 1 looks like this (always remember to put the absolute value of the largest number first):

$2x^2+3x-2x-3=0$

Group the first 2 terms together and the second 2 term together in order to factor:

$(2x^2+3x)-(2x-3)=0$ and factor out what's common in each set of parenthesis.

$x(2x+3)-1(2x+3)=0$

Notice that when we factor out a -1 from the second set of parenthesis, we can distribute it back in to get the equation we started with. We know that factoring by grouping "works" if what is inside both sets of parenthesis is exactly the same. Ours are identical: (2x + 3). That is common now, and can be factored out:

$(2x+3)(x-1)=0$