How do you solve #3(2x - 5) - 2(4x + 1) = -5(x + 3) -2#?

Question

Hazel Anglin · Accepted Answer

#x=0# Given #color(white)("XXX")color(magenta)(3(2x-5))-color(lime)(2(4x+1))=color(brown)(-5(x+3))-2# Expanding each term #color(white)("XXX")color(magenta)(""(6x-15))-color(lime)(""(8x+2))=color(brown)(""(-5x-15))-2# Combining like terms on the left and right sides #color(white)("XXX")-2x-17=-5x-17# with the obvious solution #color(white)("XXX")x=0#

Genesis Allen · Answer

undefined To solve the equation 3(2x - 5) - 2(4x + 1) = -5(x + 3) -2, first distribute the terms inside the parentheses, then combine like terms, and finally solve for x. After simplifying, the equation becomes:

6x - 15 - 8x - 2 = -5x - 15 - 2.

Combine like terms:

(6x - 8x) + (-15 - 2) = -5x - 15 - 2.

-2x - 17 = -5x - 17.

Add 5x to both sides:

-2x + 5x - 17 = -5x + 5x - 17.

3x - 17 = -17.

Add 17 to both sides:

3x - 17 + 17 = -17 + 17.

3x = 0.

Divide both sides by 3:

3x / 3 = 0 / 3.

x = 0.