Core Connections Geometry, 2013
CC
Core Connections Geometry, 2013 View details
2. Section 1.2
Continue to next subchapter

Exercise 57 Page 33

Practice makes perfect
a To solve the equation we first have to simplify the left-hand side. Note that all variables on the left-hand side are of the same kind and can therefore be combined to a single variable term.
5x-2x+x=15
4x=15
4x/4=15/4
x=3.75
b To solve for x, first want to have all x-terms on the same side. Remember inverse operations and the Properties of Equality.
3x-2-x=7-x
3x-2=7
3x=9
x=3
c Here, we first have to distribute 3 over the parentheses. After that we want to have all x-terms on one side. We do this with inverse operations and the Properties of Equality.
3(x-1)=2x-3+3x
3x-3=2x-3+3x
-3=2x-3
0=2x
2x=0
x=0
d To solve this equation, we once again have to distribute 3 over the parentheses. We also have to distribute 5 on the right-hand side.
3(2-x)=5(2x-7)+2
6-3x=5(2x-7)+2
6-3x=10x-35+2
Now, we want to have all x-terms on one side and all constants on the other side. We do this with inverse operations and the Properties of Equality.
6-3x=10x-35+2
6-3x=10x-33
-3x=10x-39
-13x=-39
x=-39/-13
x=39/13
x=3
e Notice that there is division on both sides of the equality sign. We will solve the equation by multiplying each side by the least common denominator, 57(5x), to clear denominators.
26/57=849/5x
26/57* 57(5x) = 849/5x * 57(5x)
Multiply
26(57)(5x)/57 = 849(57)(5x)/5x
26(57)(5x)/57 = 849(57)(5x)/5x
26(5x) = 849(57)
130x = 48 393
x= 372.25384...
x≈ 372.25
f Similarly as in Part E, we notice that there is division on both sides of the equation. This means we can solve the equation by multiplying each side by the least common denominator, 3(2), to clear denominators.
4x+1/3=x-5/2
Multiply
4x+1/3* 3(2)=x-5/2* 3(2)
(4x+1)(3)(2)/3 = (x-5)(3)(2)/2
(4x+1)(3)(2)/3 = (x-5)(3)(2)/2
(4x+1)(2) = (x-5)(3)
8x+2 = (x-5)(3)
8x+2 = 3x-15
Now, we will use inverse operations to isolate x.
8x+2=3x-15
5x+2=-15
5x=-17
x=-17/5
x=-3.4