Answer: Now, I'm not so sure about the identify and inconsistent part, so I took a guess. Sorry if I'm wrong!
a. x = -8 (identify)
b. x = 6 (identify)
c. x = 5 = -1 (inconsistent)
d. x = 6 (identify)
d. (the second d; it looks like there are 2 d's) x = 5 (identify)
e. 1 = -1 (inconsistent)
f. x = [tex]\frac{2}{3}[/tex] (identify)
g. x = -3 (identify)
h. 5x+5 = 5x+5 (identify)
i. I don't know, sorry :/
Step-by-step explanation:
a. 7x +5 = 2x - 35
-2x -2x (Subtract the smaller number with the x)
5x +5 = -35
-5 -5
5x = -40
x = -8 (Divide 5 with 5x and -40)
b. [tex]\frac{x}{3}[/tex] - 7 = -5
x - 21 = -15 (Multiply 3 with x/3, -7, and -5)
x = 6
c. 4x +5 = 4x -1
-4x -4x
5 = -1
d. [tex]\frac{5(x-3)}{2}[/tex] -1 = 14
10(x-3) -2 = 28 (Multiply all numbers by 2)
10x -30 -2 = 28 (Combine -30 and -2)
10x -32 = 28
+32 +32
10x = 60
x = 6
d. 3 (x-1) +2 = x+9
3x -3 +2 = x+9
3x -1 = x+9 (Subtract x from both sides b/c x is basically 1x)
-x -x
2x -1 = 9
+1 +1
2x = 10
x = 5 (Divide 2 from both sides)
e. 4x-(2x-1) = x+5+x-6
4x -2x +1 = x+5+x-6 (Mulitply the negative sign w/ 2x and -1. The negative sign is basically a -1. So, a negative times a negative is a positive)
2x+1 = 2x -1 (You can stop here or keep going)
-2x -2x
1 = -1
f. 5(2x-6)+2=(4x+3)=8x-9
10x-30+8x+6 = 8x-9
18x - 24 = 8x - 9
+24 +24
18x = 8x + 15
-8x -8x
10x = 15 (Divide 10 by both sides)
x = [tex]\frac{2}{3}[/tex]
g. [tex]\frac{2x+5}{6}[/tex] = [tex]\frac{x}{18}[/tex]
6x = 18(2x+5)
6x = 36x+90
-6x -6x
0 = 30x + 90
-90 -90
-90 = 30x (Divide 30 by both sides)
-3 = x
h. [tex]\frac{10x-4}{2}[/tex] +7 = 5(x+1)
[tex]\frac{2(5x-2)}{2}[/tex] +7 = 5(x+1) (The 2 cancels out)
5x - 2 + 7 = 5(x+1) (Combine like terms and do distributive property)
5x+5 = 5x+5 (We can stop here because each side is the same)
i. I'm so sorry, I don't quite know :/
