anonymous
  • anonymous
Solve −2(2x + 5) − 3 = −3(x − 1).
Mathematics
katieb
  • katieb
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moazzam07
  • moazzam07
-2(2x+5)-3=-3(x-1) Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides. -2(2x+5)=3-3(x-1) Multiply -3 by each term inside the parentheses (x-1). -2(2x+5)=3+(-3(x)-3(-1)) Multiply -3 by the x inside the parentheses. -2(2x+5)=3+(-3*x-3(-1)) Multiply -3 by x to get -3x. -2(2x+5)=3+(-3x-3(-1)) Multiply -3 by the -1 inside the parentheses. -2(2x+5)=3+(-3x+3*1) Multiply 3 by 1 to get 3. -2(2x+5)=3+(-3x+3) Remove the parentheses around the expression -3x+3. -2(2x+5)=3-3x+3 Add 3 to 3 to get 6. -2(2x+5)=6-3x Reorder the polynomial 6-3x alphabetically from left to right, starting with the highest order term. -2(2x+5)=-3x+6 Multiply -2 by each term inside the parentheses (2x+5). (-2(2x)-2(5))=-3x+6 Multiply -2 by the 2x inside the parentheses. (-2*2x-2(5))=-3x+6 Multiply -2 by 2x to get -4x. (-4x-2(5))=-3x+6 Multiply -2 by the 5 inside the parentheses. (-4x-2*5)=-3x+6 Multiply -2 by 5 to get -10. (-4x-10)=-3x+6 Remove the parentheses around the expression -4x-10. -4x-10=-3x+6 Since -3x contains the variable to solve for, move it to the left-hand side of the equation by adding 3x to both sides. -4x-10+3x=6 According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, x is a factor of both -4x and 3x. (-4+3)x-10=6 To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value. In this example, subtract the absolute values of -4 and 3 and give the result the same sign as the integer with the greater absolute value. (-1)x-10=6 Remove the parentheses. -x-10=6 Since -10 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 10 to both sides. -x=10+6 Add 6 to 10 to get 16. -x=16 Multiply each term in the equation by -1. -x*-1=16*-1 Multiply -x by -1 to get x. x=16*-1 Multiply 16 by -1 to get -16. x=-16 Source(s): Algebra Solved!
moazzam07
  • moazzam07
or
moazzam07
  • moazzam07
−2(2x + 5) − 3 = −3(x − 1) -4x - 10 -3 = -3x+3 -4x +3x = 3 +10 +3 -x = 16 x = -16

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anonymous
  • anonymous
Thank you very much @moazzam07
moazzam07
  • moazzam07
np

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