What is the solution set for 5(1−p)>−3p−5?

3p-1=5(p-1)-2(7-2p)

Simplifying

3p + -1 = 5(p + -1) + -2(7 + -2p)

Reorder the terms:

-1 + 3p = 5(p + -1) + -2(7 + -2p)

Reorder the terms:

-1 + 3p = 5(-1 + p) + -2(7 + -2p)

-1 + 3p = (-1 * 5 + p * 5) + -2(7 + -2p)

-1 + 3p = (-5 + 5p) + -2(7 + -2p)

-1 + 3p = -5 + 5p + (7 * -2 + -2p * -2)

-1 + 3p = -5 + 5p + (-14 + 4p)

Reorder the terms:

-1 + 3p = -5 + -14 + 5p + 4p

Combine like terms: -5 + -14 = -19

-1 + 3p = -19 + 5p + 4p

Combine like terms: 5p + 4p = 9p

-1 + 3p = -19 + 9p

Solving

-1 + 3p = -19 + 9p

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-9p' to each side of the equation.

-1 + 3p + -9p = -19 + 9p + -9p

Combine like terms: 3p + -9p = -6p

-1 + -6p = -19 + 9p + -9p

Combine like terms: 9p + -9p = 0

-1 + -6p = -19 + 0

-1 + -6p = -19

Add '1' to each side of the equation.

-1 + 1 + -6p = -19 + 1

Combine like terms: -1 + 1 = 0

0 + -6p = -19 + 1

-6p = -19 + 1

Combine like terms: -19 + 1 = -18

-6p = -18

Divide each side by '-6'.

p = 3

Simplifying

p = 3

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

∠cbe and ∠deb are same-side interior angles.

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