11) -3(1 + 6r)=14 - r\n13) -4k + 2(5k - 6)=-3k - 39\n15) 10p + 9 - 11 - p=-2(2p + 4)-3(2p - 2)\n17) 10(x +…

Explanation:

Step1: Expand the left - hand side

For the equation (-3(1 + 6r)=14 - r), use the distributive property (a(b + c)=ab+ac). So, (-3\times1-3\times6r=-3 - 18r). The equation becomes (-3-18r = 14 - r).

Step2: Add (18r) to both sides

To get all the (r) terms on one side, (-3-18r+18r=14 - r+18r), which simplifies to (-3=14 + 17r).

Step3: Subtract 14 from both sides

(-3-14=14 + 17r-14), resulting in (-17 = 17r).

Step4: Divide both sides by 17

(\frac{-17}{17}=\frac{17r}{17}), so (r=-1).

Answer:

(r = - 1)

Explanation:

Step1: Expand the left - hand side for (-4k + 2(5k - 6)=-3k - 39)

Using the distributive property (2(5k - 6)=2\times5k-2\times6 = 10k-12). The equation is (-4k+10k - 12=-3k - 39).

Step2: Combine like terms on the left - hand side

((-4k + 10k)-12=6k-12). So, (6k-12=-3k - 39).

Step3: Add (3k) to both sides

(6k+3k-12=-3k+3k - 39), which gives (9k-12=-39).

Step4: Add 12 to both sides

(9k-12 + 12=-39+12), resulting in (9k=-27).

Step5: Divide both sides by 9

(\frac{9k}{9}=\frac{-27}{9}), so (k=-3).

Answer:

(k=-3)

Explanation:

Step1: Simplify the left - hand side of (10p + 9-11 - p=-2(2p + 4)-3(2p - 2))

Combine like terms: ((10p - p)+(9 - 11)=9p-2).

Step2: Expand the right - hand side

(-2(2p + 4)-3(2p - 2)=-2\times2p-2\times4-3\times2p + 3\times2=-4p-8-6p + 6).

Step3: Combine like terms on the right - hand side

((-4p-6p)+(-8 + 6)=-10p-2).

Step4: Set up the equation

(9p-2=-10p-2).

Step5: Add (10p) to both sides

(9p+10p-2=-10p+10p-2), which gives (19p-2=-2).

Step6: Add 2 to both sides

(19p-2 + 2=-2+2), resulting in (19p=0).

Step7: Divide both sides by 19

(\frac{19p}{19}=\frac{0}{19}), so (p = 0).

Answer:

(p = 0)

Explanation:

Step1: Expand the left - hand side of (10(x + 3)-(-9x - 4)=x-5 + 3)

(10x+30 + 9x + 4=10x+9x+30 + 4=19x+34).

Step2: Simplify the right - hand side

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

Step3: Set up the equation

(19x+34=x-2).

Step4: Subtract (x) from both sides

(19x-x+34=x-x-2), which gives (18x+34=-2).

Step5: Subtract 34 from both sides

(18x+34-34=-2-34), resulting in (18x=-36).

Step6: Divide both sides by 18

(\frac{18x}{18}=\frac{-36}{18}), so (x=-2).

Answer:

(x=-2)

Explanation:

Step1: Expand both sides of (-12(x - 12)=-9(1 + 7x))

(-12x+144=-9-63x).

Step2: Add (63x) to both sides

(-12x+63x+144=-9-63x+63x), which gives (51x+144=-9).

Step3: Subtract 144 from both sides

(51x+144-144=-9-144), resulting in (51x=-153).

Step4: Divide both sides by 51

(\frac{51x}{51}=\frac{-153}{51}), so (x=-3).

Answer:

(x=-3)