To rearrange the equation v/(7x) = w/y to solve for x, you can start by multiplying both sides by 7x to eliminate the denominator on the left side. This gives you v = 7wx/y. Next, isolate x by dividing both sides by 7w/y, resulting in x = v/(7w/y), which simplifies to x = vy/(7w).
An "extraneous solution" is not a characteristic of an equation, but has to do with the methods used to solve it. Typically, if you square both sides of the equation, and solve the resulting equation, you might get additional solutions that are not part of the original equation. Just do this, and check each of the solutions, whether it satisfies the original equation. If one of them doesn't, it is an "extraneous" solution introduced by the squaring.
you do 2 sets of parenthesis and check it. for example: w2(w squared)-7w-8 (w+1) (w-8) *if you add 1w and -8w you will get -7w, which is what they want you to get. and w & w multiply to get w2(w squared), which is also what the factoring wants. another example: 3w2 (3w squared)+2-8 (3w-4) (w+2) *same thing applies with 3w x w = 3w2, and -4 +2=2, which is the answer. use this theory in all of them, unless there is a greatest common factor (GCF).
4w - 2 = -7w11w - 2 = 011w = 2w = 2/11
127w = 847w/7 = 84/7w = 12
7W + 4 - 3W = 15gather the w's together4W + 4 = 15subtract 4 from each side4W = 11divide each sides integers by 4W = 11/4================checks
56w2 + 17w - 3 = 56w2 + 24w - 7w - 3 = 8w(7w + 3) - 1(7w + 3) = (7w + 3)(8w - 1)
224
7w + 2 = 3w + 94 Subtract 3w from both sides: 4w + 2 = 94 Subtract 2 from both sides: 4w = 92 Divide both sides by 4: w = 23
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Let's start with making the variables coefficient a positive number. This obtained by simply multiply the negative fraction by -1/1, which results in the same fraction just positive. However, what you do to one side you must always do to the other. -2/7w = 8 -1/1 x -2/7w = 8 x -1/1 = 2/7w = -8 Now we see that our variable is still attached to the coefficient by means of multiplication. We must perform the inverse operation to detach the variable. In our case, division will suffice. 2/7w ÷ 2/7 = -8 ÷ 2/7 1/w = -8 ÷ 2/7 1/w = -28 w = -1/28. Is it (-2 over 7)w or -2 over (7w)?
I understand this equation to be 7w = 42. The principle we use for solving equations like this one is that we can do the same thing to both sides of the equation and the equation will still be _true_. We want the 'w' by itself. This implies ridding the left side of the 7. We can turn it into a one (1) by dividing it by 7. But if we do that to the left side of the equation then we must also do that to the right side. 7w/7 = 42/7 1w = 6 or w = 6, the result.
-63=7w
-4
16