How Would You Find 2x 2 1/3 Using Distributive Property

Do the math problems 4+ 2 (x-3) = 6 and 2(x-3) +4 = 6 have the same answer for x? If so, why?

YES, the two given equations, 4 + 2(x - 3) = 6 and 2(x - 3) + 4 = 6, have the same answer or solution, i.e., they have the same value for the variable x. Let's solve each equation and see.Equation (1.): 4 + 2(x - 3) = 6Using the Distributive Property to perform the indicated multiplication on the left side, we get: 4 + 2(x) - 2(3) = 64 + 2x - 6 = 62x + 4 - 6 = 62x - 2 = 6 Now, adding 2 to both sides to begin isolating x on the left side, we have:2x - 2 + 2 = 6 + 22x + 0 = 82x = 8Now, divide both sides by 2 in order to isolate the variable x, thus finally solving the equation for x:(2x)/2 = 8/2(2/2)x = 8/2(1)x = 4x = 4Equation (2.): 2(x - 3) + 4 = 62(x) - 2(3) + 4 = 62x - 6 + 4 = 62x - 2 = 6Now, adding 2 to both sides to begin isolating x on the left side:2x - 2 + 2 = 6 + 22x + 0 = 82x = 8Now, divide both sides by 2 in order to isolate the variable x, thus finally solving the equation for x:(2x)/2 = 8/2(2/2)x = 8/2(1)x = 4x = 4As seen above, the two given equations, 4 + 2(x - 3) = 6 and 2(x - 3) + 4 = 6, do indeed have the same solution, i.e., they have the same value for the variable x, x = 4, because the respective sides of the two equations are equal to each other, that is, the left sides equal each other, and the right sides equal each other.To prove this, let's first take a look at the two left sides:4 + 2(x - 3) = 2(x - 3) + 4 because of the Commutative Property of Addition which says that for any two numbers "a" and "b," a + b = b + a, i.e., regardless of the order in which two numbers are added, the resultant sum is the same. In this case, a = 4 and b = 2(x - 3).Now, let's look at the two right sides:Obviously, 6 = 6 because of the Reflexive Property of Equality which says that for any number "a," a = a.Therefore, this is why the two given equations have the same solution or the same value for x.

What's solution for (5X+6) (X-1) -(2X^2-5X+3) =0?

In order for this to be true, then both sides of the minus sign - must cancel each other out to equal 0.First, use the FOIL method for the pair of binomials on the far left:(5x + 6)(x-1) - (2x^2 - 5x + 3) = 0(5x^2 - 5x + 6x - 6) - (2x^2 - 5x + 3) = 0Combine like terms:(5x^2 + x - 6) - (2x^2 - 5x + 3) = 0Now distribute the negative sign to the trinomial on the right, and then drop the parentheses and combine like terms:(5x^2 + x - 6) - 2x^2 + 5x - 3 = 03x^2 + 6x - 9 = 0Factor out the 3 as a common factor in all three terms:3(x^2 + 2x - 3) = 0And finally, factor the trinomial:3(x + 3)(x-1) = 0Now, there are two possible solutions for x that will make this a true statement:x = -3x = 1Substitute for x, for both solutions, to verify this:x = -33(-3 + 3)(-3 - 1) = 03(0)(-4) = 00(-4) = 00 = 0x = 13(1+3)(1–1) = 03(4)(0) = 012(0) = 0Finally, go back to the original equation you posted and try both values for x in it:(5x+6)(x-1) - (2x^2 - 5x + 3) = 0Right off the bat I can tell you that these terms should cancel each other out to equal 0. It’s also possible only one of the solutions we came to might work. But let’s try both out and see what happens.x = -3(5*-3+6)(-3–1) - (2*-3^2 - 5*-3 + 3) = 0(-15 + 6)(-4) - (2*9+15+3) = 0(-9)(-4) - (18+15+3) = 036 - (36) = 00 = 0So x = -3 is a valid solution to this equation. Now let��s try the other solution:x = 1(5*1+6)(1–1) - (2*1 - 5*1 + 3) = 0(5+6)(0) - (2–5+3) = 011(0) - (-3+3) = 00 - 0 = 0So there are two solutions for x:x|x:(-3,1)

How do I solve this: (√3-1) * (√3+1)?

Here are two methods on how to solve the given multiplication problem: (1.)   You could use the Column Method.  This method is a good way to organize your work as you’re multiplying the two expressions.  Be careful to keep like-radical terms (those that have the same index and the same radicand) in the same column as follows:  (√3 –  1)(√3 + 1)  =  √3  +  1                                      √3  –  1                                         √9 + √3        (partial product of √3 times √3 + 1)                                            –√3 – 1  (partial product of – 1 times √3 + 1)                                     √9 +  0   – 1 =  3 – 1                                                                = 2  (product) (2.)   The Distributive Property can also be used to multiply the two given expressions as follows: (√3 – 1)(√3 + 1) = √3(√3 –  1) + 1(√3 – 1)                               = √3√3 – (1)√3 + (1)√3 + 1(–1)                               = √9 + (– √3 + √3) + (–1)                               = 3 + (0) + (– 1)                               = 3 + (– 1)                               = 2

How do I solve X (4x+5) +3 (2x^2-4x+1) in steps? My answer key says 10x^2-7x+3 and I'd like to know how they got that answer?

Let’s break the question into 2 parts. Often doing so will hide the complexity of the question until it convenient with which to deal.So, [math]x(4x+5)=4x^2+5x.[/math] I don’t know if FOIL is fashionable these days. It mention First, Outside, Inside Last and is a mnemonic for multiplying pairs of brackets. Here, since there was only one bracket, we used FO (not being rude)Then [math]3(2x^2-4x+1)=6x^2-12x+3.[/math] This time, FOIL is not long enough, so use the real rule which is more like multiply everything here by everything there.Now, in order to add the two answers together, group them as follows,[math](4x^2+6x^2)+(5x-12x)+3=10x^2-7x+3.[/math]Sometimes brackets are used for nothing more than organizing and directing focus, don’t be afraid to use them.