Use the equation 10x+18=48 for parts a-d?

Question

a. Add 4 to each side of the equation. Tell, how you know that the two sides are still equal.
b. How are the solutions of the original equation and the equation in part a related? What does the term EQUIVLENT EQUATIONS mean?
c. Use subtraction, multipacation and divison to form three equations equivlent to the to the orignal equation.
d. Solve the original equation. Explain the step in finding the solution.

Answer 1

Okay, this is just algebra. I'll try to explain everything.

1) 10x+18+4=48+4
10x+22=52

These are still equal because you added 4 to both sides. This means that you can subtract 4 from both sides and end up with the original equation. The point is that you can add any number you want, as long as you add it to both sides. That way the equations remains the same, as the numbers you added "cancel out."

2) They are the same. The solution for the original equation is the same as the solution for the equation in part a. "Equivalent equations" means that the solution set (the points of intersection, the values that fit both equations) are all numbers x. In this case, the equations (original and in part a) are equivalent. Equivalent equations are the same equations graphically (when you graph them).

3) Subtraction: Here I subtracted 1 from both sides
10x+18-1=48-1
10x+17=47

Division: Here I divided each side by 2 (which is the same as multiplying by 1/2)
1/2(10x+18)=1/2(48)
5x+9=24

Multiplication: Here I multiplied each side by 2
2(10x+18)=48
20x+36=96

d) This isn't too hard. Let's solve it.
10x+18=48

Subtract 18 from both sides
10x+18-18=48-18

Simplify
10x=30

Divide both sides by 10.
x=3


That's your answer.


Hope this helps.

Answer 2

a. because if you do the same thing to both sides, if they started out equal they will remain equal.
b. they are increased by 4. equivelent equations means theat two equations have the same answer.
c. 48-18=10x
48/10=x+18
48/x=10+18

d. 10x+18=48
-18 = -18 first subtract 18 from both sides
10x = 30
/10 = /10 divide 10 from both sides
x = 3

Answer 3

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