Solve for x. round to nearest tenth if needed.

1. 7r-7=2r+18

a. r=-5
b. r=5
c. r=2.2
d. r=1.2

2. 2x+12=18-x

a. x=3
b. x=10
c. x=6
d. x=2

3. 8x-3=15x+18

a. x=-3
b. x=3
c. x=2.1
d. x=0.9

4. 6y-6=4y+16

a. y=2.2
b. y=-2.2
c. y=11
d. y=5

5. 3(x-4)=5(x+2)

a. x=11
b. x=-11
c. x=1
d. x=-1

1)  The answer is: [B]: r = 5 .

Explanation:
 
Given: 7r − 7 = 2r + 18 ; Round your answer to the nearest tenth, if necessary.

Since "r" is the only variable given, let us assume we want to solve for "r" (instead of "x").

→ Subtract "2r" from EACH SIDE of the equation; and & add "7" to EACH SIDE of the equation:

→ 7r − 7 − 2r + 7 = 2r + 18 − 2r + 7 ;  to get: → 5r = 25 ;

→ Now, divide EACH SIDE of the equation by "5"; to isolate "r" on one side of the equation; and to solve for "r" :

→ 5r / 5 = 25 / 5 → r = 5 → which is: "Answer choice: [B]".

Let us check our answer, by plugging in "5" for "r" in the original equation:

 → 7r − 7 = 2r + 18 ;  →  7(5) − 7 =? 2(5) + 18? ;

→ 35 − 7 =? 10 + 18 ?;     → 28 =? 28? Yes!

 2) The answer is: [D]: x = 2 .

Explanation: 

Given: 2x + 12 = 18 − x ; Solve for "x" (round to nearest tenth, if necessary).

→ Add "x" to EACH SIDE of the equation, & subtract "12" from EACH SIDE of the equation:  → 2x + 12 + x − 12 = 18 − x + x − 12 ; 

→ To get: 3x = 6 ;  → Divide EACH SIDE of the equation by "3";
to isolate "x" on one side of the equation; and to solve for "x":

→ 3x / 3 = 6 / 3 ; → x = 2 ; which is: "Answer choice: [D]".

Let us check our answer, by plugging in "2" for "x" in the original equation:

→ 2x + 12 = 18 − x ; → 2(2) + 12 =? 18 − 2 ?

→ 4 + 12 =? 18 − 2 ? ;   → 16 =? 16?  Yes!

3)  The answer is: [A]: x = -3 . 

Explanation:

Given:  8x − 3 = 15x + 18 ; Solve for "x". Round your answer to the nearest tenth, if necessary.

→ Subtract "8x" from EACH SIDE of the equation, & add "3" to EACH SIDE of the equation:

→ 8x − 3 − 8x + 3 = 15x + 18 − 8x + 3 ; to get:

→ 0 = 7x + 21 ; → Subtract "21" from EACH SIDE of the equation;

→ 0 − 21 = 7x + 21 − 21 ; to get:

→  -21 = 7x ; Now divide EACH SIDE of the equation by "7";
    to isolate "x" on one side of the equation; & to solve for "x":

→ = -21 / 7 = 7x / 7 ; →  -3 = x ; which is "Answer choice: [A]."

Let us check our answer, by plugging in "-3" for "x" in the original equation:

→  8x − 3 = 15x + 18 ;  → 8(-3) − 3 =?  15(-3) + 18 ?;

→ -24 − 3 =?  -45 + 18 ? ;   →  -27 =? -27?  Yes!

4)  The answer is: [C]: y = 11 .

Explanation:

Given: 6y − 6 = 4y + 16 ; Solve for "y"; Round to the nearest tenth, if necessary.

(Note: Since "y" is the only variable given; assume we are to solve for "y" instead of "x").

→ Subtract "4y" from EACH SIDE of the equation, & add "6" to EACH SIDE of the equation; → 6y − 6 − 4y + 6 = 4y + 16 − 4y + 6 ; to get:

→ 2y  = 22 ; Now, divide EACH SIDE of the equation by "2"; to isolate "y" one side of the equation; and to solve for "y" ;

→ 2y / 2 = 22 / 2 ; →  y = 11 → which is "Answer choice: [C]".

Let us check our answer, by plugging in "11" for "y" in the original equation:

→  6y − 6 = 4y + 16 ; → 6(11) − 6 =? 4(11) + 16 ?

→ 66 − 6  =? 44 + 16 ?  → 60 =? 60 ?  Yes!

5)  The answer is: [B]: x = -11 .

Explanation:

Given: 3(x − 4) = 5(x + 2) ; Solve for "x". Round to the nearest tenth, if necessary.

→Note the "distributive property of multiplication": 

a*(b + c) = ab + ac ;  and: a*(b − c) = ab − ac ;

→ Let us expand EACH SIDE of our given equation.
→Start with the "left-hand side":

3(x − 4) = (3*x)  − (3*4) = 3x − 12;

→Now let us expand the "right-hand side" of the given equation:

→  5(x + 2) = (5*x) + (5*2) = 5x + 10 ;

→Now, we can rewrite the original equation:

→ 3(x − 4) = 5(x + 2) ; by substituting the expanded values for EACH SIDE of the question:   →  3x − 12 = 5x + 10 ;

→ Subtract "3x" from EACH SIDE of the equation; and add "12" to EACH SIDE of the equation: →  3x − 12 − 3x + 12 = 5x + 10 − 3x + 12 ; to get:

→  0 = 2x + 22;  → Now subtract "22" from EACH SIDE of the equation:

→  0 − 22 = 2x + 22 − 22 ; to get:  →  -22 = 2x ;

→ Divide EACH SIDE of the equation by "2"; to isolate "x" on one side of the equation; & to solve for "x" ;

→  -22 / 2 = 2x /2 ;  →  -11 = x ; which is "Answer choice: [B]".

Let us check our answer, by plugging in "-11" for "x" in the original equation:

→ 3(x − 4) = 5(x + 2) ; →  3(-11 − 4) =? 5(-11 + 2) ? ; 

→3(-15) =? 5(-9) ? ; → -45 =? -45 ?  Yes!

Hope these answers and explanations are helpful. Best of luck!