Question

Solve for p. 2(p+ 5) = 16

Solve for t. -3(t + 1) = 18

Solve for x -2/5 (x+10)=-10

Solve for x. 2/3 (x -10)=-2

Answer 1

Answer:

1) $p=3$

2)$t=-7$

3)$x=15$

4) $x=7$

Step-by-step explanation:

1) Apply distributive property:

$2(p+ 5) = 16\\2p+10=16$

Subtract 10 from both sides of the equation and then divide both sides by 2:

$2p+10-10=16-10\\\frac{2p}{2}=\frac{6}{2}\\p=3$

2) Apply distributive property:

$-3(t + 1) = 18\\-3t -3= 18$

Add 3 to both sides of the equation and then divide both sides by -3:

$-3t -3+3= 18+3\\\frac{-3t}{-3}=\frac{21}{-3}\\t=-7$

 3) Apply distributive property:

$-\frac{2}{5}(x+10)=-10\\\\-\frac{2}{5}x-4=-10$

Add 4 to both sides of the equation:

$-\frac{2}{5}x-4+4=-10+4\\\\-\frac{2}{5}x=-6$

Multiply both sides by $-\frac{5}{2}$:

$(-\frac{2}{5}x)(-\frac{5}{2}) =-6(-\frac{5}{2})\\\\x=15$

4) Apply distributive property:

$\frac{2}{3}(x-10)=-2\\\\\frac{2}{3}x-\frac{20}{3}=-2$

 Add $\frac{20}{3}$ to both sides of the equation:

$\frac{2}{3}x-\frac{20}{3}+\frac{20}{3}=-2+\frac{20}{3}\\\\\frac{2}{3}x=\frac{14}{3}$

Multiply both sides by $\frac{3}{2}$:

$(\frac{2}{3}x)(\frac{3}{2})=(\frac{14}{3})(\frac{3}{2})\\\\x=7$

Answer 2

Hello!

The answers are:

1 $p=3$

2 $x=-7$

3 $x=35$

4 $x=7$

Why?

To know the solution of the problems, we need to isolate each variable.

Remember that:

-  If we have  an equality:  if the number is part of a product , and if you need to move it to the other side of the equality, the same number will be dividing the factors of the side.

- If we have an equality: if the number is subtracting (negative sign), and if you need to move it to the other side of the equality, its sign changes to positive.

- If we have an equality: if the number is adding (positive sign), and if you need to move it to the other side of the equality, its sign changes to negative.

- The distributive property states that:

$a(b+c)=ab+ac$

So,

1 - Solving for p

$2(p+5)=16\\2p+10=16\\2p=16-10=6\\p=\frac{6}{2}=3$

2 - Solving for t

$-3(t+1)=18\\-3t-3=18\\-3t=18+3=21\\t=\frac{21}{-3}=-7$

3 - Solving for x

$-\frac{2}{5}(x-10)=-10\\-\frac{2}{5}x+\frac{2}{5} *10=-10\\-\frac{2}{5}x+4=-10 \\-\frac{2}{5}x=-10-4=-14\\-\frac{2}{5}x=-14\\x=\frac{-14}{\frac{-2}{5} }=14*\frac{5}{2}=35$

4 - Solving for x

$\frac{2}{3}(x-10)=-2\\\\x-10=\frac{-2}{\frac{2}{3} }=-2*\frac{\\3}{2}\\\\x-10=-3\\x=-3+10\\x=7$

Have a nice day!