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Topic: **Problem solving homework****Question:**
how do you solve this problem step by step?
i dont know how to do it and its on my homework.
5x + 7 = 3x - 5
thanks

June 17, 2019 / By Poppy

Add 5 to both sides 5x + 12 = 3x Subtract 3x from both sides 2x + 12 = 0 Subtract 12 from both sides 2x = -12 Divide both sides by two x = -6 Lather, rinse, repeat on the next problem.

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Brackets first (5+20/2*5) Then division is first. 20/2 =10 10*5 =50 5+50=55 2*55 =110 10+110=120 Now on the other side of the minus sign. There is both multiplication and division. Since you did division first on the left, do division first. 2/2 =1 2*1*2 =4 Therefore 120-4 = 116

The correct answer is 116 but you need to use the proper algebraic priorities. Think of this acronym to help you remember: BIDMAS Brackets Indeces Division & Multiplication Addition & Subtraction Remember addition and subtraction last. So let's look at 2^(5+20/2^5) right the brackets are evaluated first but within the brackets we have a multiplication and division, so we do the multiplication first 2*5 = 10 20/2 = 10 10*5 = 50 (if you wanted to do 20/10 you needed to have the 2*5 bit in brackets otherwise teh 20 is divided by 2 and then the result multiplied by 5 as division and multiplication are on the same priority) 5+50 = 55 2*55 = 110 10+ 110 = 120 now for the subtraction 2*2 =4 4/2 = 2 2*2 =4 Therefore our whole expression simplifies to 120-4 = 116 Hope this helps.

First: combine "like" terms - subtract 3x from both sides (when you move a term to the opposite side, always use the opposite sign). 5x -3x + 7 = 3x -3x - 5 5x -3x + 7 = - 5 2x + 7 = - 5 SEc: subtract 7 from both sides... 2x + 7 - 7 = - 5 - 7 2x = - 5 - 7 2x = - 12 Third: solve "x" by isolating it - divide each term by 2. 2x/2 = - 12/2 x = -12/2 x = - 6

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F = multiply the first number in each set of parenthesis O = multiply the outside number in each set of parenthesis I = multiply the Inside number in each set of parenthesis L = multiply the last number in each set of parenthesis Then all you have to do is clean it up and combine like-terms. F ---> 5b x 5b = 25b squared O ---> 5b x -3g = -15bg I ---> 3g x 5b = 15bg L ---> 3g x -3g = -9g squared ANSWER -------> 25bsquared - 9g squared I really hope this helps you out. This is probably the best I can explain it.

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half life is defined as the time it takes for 1/2 the material to decay. For material such as plutonium, the decay rate is proportional to the amount of substance , so more the material faster it decays. However the rate slows down as the material keeps decaying so our logic is that in every 24360 years half the plutonium remaining decays away. like, 100 grams becomes 50 grams in 24360 years, 50 becomes 25 after another 24360 years and so on. to use algebra , let us consider 24360 years as a period. In one period (p=1) weight (w)=100/2=50 in 2 periods (p=2) 50/2=100/4=25 and so on So in n periods w=100/2^n lets assume this formula for all values of n let weight=75g in x periods then 75=100/2^x gives 2^x=100/75 gives 2^x=4/3 taking log on both sides xlog2=log4-log3 x=(log4-log3)/log2=0.415 periods no of years = 0.415*24360=10109 years the justification to use the equation w=100/2^n answer can really only be found using calculus (sovling the differential equation dw/dt=-kw where k is a constant), yielding w(t)=we^-λt where w is the initial quantity of the substance that will decay (this quantity may be measured in grams, moles, number of atoms, etc.), w(t) is the quantity that still remains and has not yet decayed after a time t, t1 / 2 is the half-life of the decaying quantity, τ is a positive number called the mean lifetime of the decaying quantity, λ is a positive number called the decay constant of the decaying quantity. The three parameters t1 / 2, τ, and λ are all directly related in the following way: half life t1/2= ln(2)/λ=τ*ln(2) here half life = 24360=ln(2)/λ λ=ln(2)/24360=0.693/24360=2.844*10^-5 now using this equation to compare weight 75=100e^-λt gives 0.75=e^-λt take natural log on both sides ln(0.75)=-λt t=0.287/λ=0.287/(2.844*10^-5)=10091 years. Yields pretty much the same answer. Must be remembered that both the equations are pretty much the same.

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