## spidergirl51 3 years ago Write an equation and solve. Four times the sum of three times a number increased by two is equal to three times the difference of two times the number decreased by eight. What is the number?

1. gallaxhar

Solve for x: 4 (2+3 x) = 3 (2 x-8) Write the linear polynomial on the left hand side in standard form. Expand out terms of the left hand side: 8+12 x = 3 (2 x-8) Write the linear polynomial on the left hand side in standard form. Expand out terms of the right hand side: 8+12 x = 6 x-24 Move terms with x to the left hand side. Subtract 6 x from both sides: (12 x-6 x)+8 = (6 x-6 x)-24 Add like terms in 12 x-6 x. 12 x-6 x = 6 x: 6 x+8 = (6 x-6 x)-24 Look for two terms that sum to zero. 6 x-6 x = 0: 6 x+8 = -24 Isolate terms with x to the left hand side. Subtract 8 from both sides: 6 x+(8-8) = -24-8 Look for two terms that sum to zero. 8-8 = 0: 6 x = -24-8 Evaluate -24-8. -24-8 = -32: 6 x = -32 Solve for x. Divide both sides of 6 x = -32 by 6: x = (-32)/6 Cancel down (-32)/6. Express (-32)/6 in its lowest form by cancelling out True from the numerator and denominator. (-32)/6 = (2 (-16))/(2×3) = -16/3: Answer: x = (-16)/3

2. spidergirl51

wow

3. spidergirl51

i am not sure i thought there was no solutuion>

4. gallaxhar

the answer is definitely x = (-16)/3

5. gallaxhar

just work through the above steps

6. spidergirl51

you are right your really smart u know htat

7. gallaxhar

no not really. it just looks that way because it's like seeing someone speak Chinese if you don't know Chinese, you will think it's pretty complicated. It is complicated if you try to speak Chinese and don't know it, but it's a bunch of logical building blocks (words, definitions) bundled together in a certain order. Math is a language no different than Chinese or English, if you focus on learning the building blocks it won't be confusing or frustrating to you any longer. It won't make you smarter than another person necessarily it will just mean you speak another language proficiently.