Step-by-step explanation:
A IS THEM ANSWER
Answer:
x = -30
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define Equation</u>
0.2(4x + 10) - 0.9x = 0.2(x - 6) + 12.2
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute 0.2: 0.8x + 2 - 0.9x = 0.2x - 1.2 + 12.2
- Combine like terms: -0.1x + 2 = 0.2x + 11
- Add 0.1x on both sides: 2 = 0.3x + 11
- Isolate <em>x </em>term: -9 = 0.3x
- Isolate <em>x</em>: -30 = x
- Rewrite: x = -30
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: 0.2(4(-30) + 10) - 0.9(-30) = 0.2(-30 - 6) + 12.2
- Multiply: 0.2(-120 + 10) + 27 = 0.2(-30 - 6) + 12.2
- Add/Subtract: 0.2(-110) + 27 = 0.2(-36) + 12.2
- Multiply: -22 + 27 = -7.2 + 12.2
- Add: 5 = 5
Here we see that 5 does indeed equal 5.
∴ x = -30 is the solution to the equation.
Answer:
20 dollars an hour.
Step-by-step explanation:
Anamarie worked for 21 hours. 420 dollars divided by 21 hours is 20 dollars per hour. Since she worked for 3 hours each night and she worked for 21 hours she worked 7 nights ergo 1 week.
Answer:
![\boxed{\bold{Both \ Sides \ Are \ Equal, \ True \ For \ All \ x}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cbold%7BBoth%20%5C%20Sides%20%5C%20Are%20%5C%20Equal%2C%20%5C%20True%20%5C%20For%20%5C%20All%20%5C%20x%7D%7D)
Step By Step Explanation:
Expand ![\bold{5\left(-3x-2\right)-\left(x-3\right): \ -16x-7}](https://tex.z-dn.net/?f=%5Cbold%7B5%5Cleft%28-3x-2%5Cright%29-%5Cleft%28x-3%5Cright%29%3A%20%5C%20-16x-7%7D)
Expand ![\bold{-4\left(4x+5\right)+13: \ -16x-7}](https://tex.z-dn.net/?f=%5Cbold%7B-4%5Cleft%284x%2B5%5Cright%29%2B13%3A%20%5C%20-16x-7%7D)
![\bold{-16x-7=-16x-7}](https://tex.z-dn.net/?f=%5Cbold%7B-16x-7%3D-16x-7%7D)
Add 7 To Both Sides
![\bold{-16x-7+7=-16x-7+7}](https://tex.z-dn.net/?f=%5Cbold%7B-16x-7%2B7%3D-16x-7%2B7%7D)
Simplify
![\bold{-16x=-16x}](https://tex.z-dn.net/?f=%5Cbold%7B-16x%3D-16x%7D)
Add 16x To Both Sides
![\bold{-16x+16x=-16x+16x}](https://tex.z-dn.net/?f=%5Cbold%7B-16x%2B16x%3D-16x%2B16x%7D)
Simplify
![\bold{0=0}](https://tex.z-dn.net/?f=%5Cbold%7B0%3D0%7D)
- Both Sides Are Equal, True For All x
- Mordancy
5 x (6-3) + 10/ (8-3)
5 x (3) + 10/ (5)
15+2
17