1. 4(2+3c) = 56
c = 4
3. -29 = 5(2a-1)+2a
a = -2
5 . 7p-(3p+4) = -2(2p-1)+10
p=2
7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)
x=4
Step-by-step explanation:
1. 4(2+3c) = 56
Subtracting 8 from both sides
Dividing both sides by 12
<u>Checking: </u>
![4[2+3(4)] = 56\\4(2+12) = 56\\4(14) = 56\\56 = 56](https://tex.z-dn.net/?f=4%5B2%2B3%284%29%5D%20%3D%2056%5C%5C4%282%2B12%29%20%3D%2056%5C%5C4%2814%29%20%3D%2056%5C%5C56%20%3D%2056)
3. -29 = 5(2a-1)+2a
Simplifying
Adding 5 on both sides
Dividing both sides by 12
<u>Checking:</u>
![-29 = 5(2a-1)+2a\\-29 = 5[2(-2)-1]+2(-2)\\-29 = 5(-4-1) -4\\-29 = 5(-5) -4\\-29 = -25-4\\-29 = -29](https://tex.z-dn.net/?f=-29%20%3D%205%282a-1%29%2B2a%5C%5C-29%20%3D%205%5B2%28-2%29-1%5D%2B2%28-2%29%5C%5C-29%20%3D%205%28-4-1%29%20-4%5C%5C-29%20%3D%205%28-5%29%20-4%5C%5C-29%20%3D%20-25-4%5C%5C-29%20%3D%20-29)
5 . 7p-(3p+4) = -2(2p-1)+10
Simplifying
Adding 4 on both sides
Adding 4p on both sides
Dividing both sides by 8
<u>Checking:</u>
![7p-(3p+4) = -2(2p-1)+10\\7(2)-[3(2)+4] = -2[2(2)-1] +10\\14 - (6+4) = -2 (4-1) +10\\14 - 10 = -2(3) +10\\4 = -6+10\\4=4](https://tex.z-dn.net/?f=7p-%283p%2B4%29%20%3D%20-2%282p-1%29%2B10%5C%5C7%282%29-%5B3%282%29%2B4%5D%20%3D%20-2%5B2%282%29-1%5D%20%2B10%5C%5C14%20-%20%286%2B4%29%20%3D%20-2%20%284-1%29%20%2B10%5C%5C14%20-%2010%20%3D%20-2%283%29%20%2B10%5C%5C4%20%3D%20-6%2B10%5C%5C4%3D4)
7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)
Simplifying
Adding 6 on both sides
Subtracting 3x from both sides
Dividing both sides by 6
<u>Checking:</u>
![\frac{1}{2} [-4+6(4)] = \frac{1}{3}(4)+\frac{2}{3}(4+9)\\\frac{1}{2}(-4+24) = \frac{4}{3}+\frac{2}{3}(13)\\\frac{1}{2}(20) = \frac{4}{3} +\frac{26}{3}\\15 = \frac{4+26}{3}\\15 = \frac{30}{3}\\15=15](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5B-4%2B6%284%29%5D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%284%29%2B%5Cfrac%7B2%7D%7B3%7D%284%2B9%29%5C%5C%5Cfrac%7B1%7D%7B2%7D%28-4%2B24%29%20%3D%20%5Cfrac%7B4%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B3%7D%2813%29%5C%5C%5Cfrac%7B1%7D%7B2%7D%2820%29%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%2B%5Cfrac%7B26%7D%7B3%7D%5C%5C15%20%3D%20%5Cfrac%7B4%2B26%7D%7B3%7D%5C%5C15%20%3D%20%5Cfrac%7B30%7D%7B3%7D%5C%5C15%3D15)
Keywords: Linear equations
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#LearnwithBrainly
Hey there!
We're going to write the equation for this line in slope-intercept form, y = mx+b, where m is the slope and b is the y-intercept. In order to write it in this form, as stated in the name, we need the slope and y-intercept. Since we have the slope given, we can use the points we have and set up that equation with the given slope to solve for b. We'll use the x and y values and throw them into the equation. We have:
-1 = 3/2(4) + b
-1 = 12/2 + b
-1 = 6 + 6
-6 = b
Now, since we have our slope and y-intercept, we can write our equation with these two values:
y = 3/2x - 6
Hope this helps!
To find the inverse we have to first change the function notation to 'y'
So
f(x) = -x becomes y = -x
Next, we have to switch the x and y values
So, y = -x becomes x = -y
Now, we have to solve for y.
y = -x
So the inverse of f(x) = -x is:
2(x+4)+2(2x-8)
2x+8+4x-16
=6x-8
3 * 0.28 + 0.38y = the total cost
Step-by-step explanation:
