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Check this answer (and every answer on this test) on the next slide. 1) When there is a number or variable right next to a parenthesis without an operational sign, it is understood to be multiplication. Therefore, we have to multiply that number or variable by everything inside the parentheses. Ex: 3(x + 4) = 3x + 12 4(2x - 3) = 8x - 12 -(x + 3) = -x - 3
What would 4(x + 5) equal? 4x + 5 4x - 5 4x + 20 4x - 20 Answer to previous question: 4(x + 5) = 4x + 4•5 4x + 20 When there is a number or variable right next to a parenthesis without an operational sign, it is understood to be multiplication. Therefore, we have to multiply that number or variable by everything inside the parentheses. Ex: 3(x + 4) = 3x + 12 4(2x - 3) = 8x - 12 -(x + 3) = -x - 3
6x + 12 6x - 12 2) What would 3(2x + 4) equal? 3x + 4 2x + 12 Answer to previous question: 3(2x + 4) = 3•2x + 3•4 6x +12
3) What would 3(2x - 4) equal? 6x + 12 6x - 12 3x + 4 2x + 12 Answer to previous question: 3(2x -4) = 6x - 12
4) What would 3(-x - 4) equal? 6x + 12 6x - 12 -3x - 12 2x + 12 Answer to previous question: 3(-x - 4) = -3x - 12
5) What would -3(-x - 4) equal? 6x + 12 6x - 12 -3x - 4 3x + 12 Answer to previous: -3(-x -4) = 3x + 12
3x + 4x = 21 has variables on the same side of the equal side. They can be combined to make 7x = 21.
Where 3x = 4x + 21 variables on different sides. -4x needs to be added to both sides to clear it from the side with the number so that variables are on one side and the numbers are on the other side.
6) On 5 = 2x + 3x what needs to be done first? 2x + 3x can be combined to make 5 = 5x -2x can be added to both sides to make 5 - 2x = 3x Previous answer: 2x + 3x is combined to make 5x.
We combine like variables or numbers on the same side on an equation following the signs. We move variables or numbers to the other side by adding their opposites to both sides.
Combine like terms 7) On 5 - 2x = 3x what needs to be done first?
Move variables to one side and numbers to the other Answer to previous question: 5 - 2x = 3x +2x +2x 5 = 5x "Move variables to one side" 5 5 x = 1
Combine like terms Move variables to one side and numbers to the other
8) On 4x = 3x - 9 what needs to be done first? Answer to previous question: 4x = 3x - 9 "Move variables to one side" -3x -3x x = -9 Combine like terms Move variables to one side and numbers to the other 9) On 4x + 3x = 21 what needs to be done first? Combine like terms Answer to previous question: On 4x + 3x = 21 what needs to be done first? Combine like terms 4x + 3x to get 7x 7x = 21 7 7 x = 3
10)What needs to be done first on 3x + 5 - 8 = 9? Move variables to one side and numbers to the other Combine like terms Move variables to one side and numbers to the other Answer to previous question: What needs to be done first on 3x + 5 - 8 = 9?
Combine like terms + 5 - 8 to get -3 3x -3 = 9 Then move numbers to one side +3 +3 by adding the opposite of -3 3x = 12 3 3 Now clear multiplication with division x = 4 11) What needs to be done first on 2x - 4 = 9? 6 Answer to previous question: What needs to be done first on 2x - 4 = 9? Move variables to one side and numbers to the other by adding the opposite of -4 to both sides. 2x -4 = 9 +4 +4 2x = 13 2 2 x = 6.5 or 6 1/2 or 13/2 12) Solve: 2x = -3x + 30 5 -5 -6 Answer to previous question: Solve 2x = -3x + 30 +3x +3x to move variables to one side 5x = 30 5 5 to undo multiplication x = 6
13) Solve: 3x + 7 = 2x + 2 -3 5 -5 3 -3 Answer to previous question: Solve 3x + 7 = 2x + 2 Move variables to one side -2x -2x by -2x from both sides x +7 = 2 Move numbers to other -7 -7
x = -5
14) Solve: 2(x + 3) = -4x - 12 5 -5 3 Distribute Answer to previous question: Solve: 2(x + 3) = -4x - 12 Distribute 2 first 2x + 6 = -4x - 12 +4x +4x Move variables to one side
6x + 6 = -12 Numbers to the other side -6 -6 6x = -18 Clear multiplication with division
What operation was the final step? 6 x = -3 6 Move variables Division Answer to previous question: 1st Step: Distribute 2nd Step: Combine any like terms on the same side 3rd Step: Variables to one side 4th Step: Numbers to the other side 5th Step: Clear multiplication or division w/inverse
16) Solve: + 5 = 3 6 3 x -6 -2 -2 Answer to previous question:
Solve: + 5 = 3 -5 to both sides -5 -5
= -2 Multiply both sides by 3
x = -6
17) Solve: + 4 = 8 8 3 * x 3 x 3 -2 -24 x * 3 -8 24 20 18) - 4 = -8 Answer to previous question:
Solve: + 4 = 8 -4 to both sides
-4 -4
= 4 Multiply both sides by -2
x = -8
-2 • -2 -2 x x -5 x -24 • -2 -20 24 60 Answer to previous question:
Solve: - 4 = -8 +4 to both sides
+4 +4
= -4 Multiply both sides by -5
x = 20
19) Solve: + 4 = -8 -5 * -5 x -5 x -5 -24 x * -5 -60 24 60 Answer to previous question:
Solve: + 4 = -8 Add -4 to both sides -4 -4
= -12 Multiply both sides by -5
x = 60
20) Solve: - x + 3 = 7
-5 * -5 -5 x x -24 1 6 * -5 -60 24 -33 Answer to previous question: Solve: - x + 3 = 7 Add -3 to both sides -3 -3
x = 4 we can not divide fractions x = -24 multiply by the reciprocal
21) Solve: x + 3 = -8 -6 * 6 1 6 1 -2 3 1 * -6 33 2 6 Answer to previous question:
Solve: x + 3 = -8 -3 to both sides to move #'s -3 -3
x = -11 Multiply by the reciprocal
x = -33
22) Solve: x + 3 = 7 3 * 3 1 3 1 3 2 -6 * 3 9 -9 Answer to previous question:
Solve: x + 3 = 7 -3 to both sides to move #'s -3 -3
x = 4 Multiply by the reciprocal
x = 6
23) Solve: (x -6) = 2 6 3 * 2 3 3 2 2 2 3 -6 * 3 2 9 -9 10 Answer to previous question:
Solve: (x - 6) = 2 Multiply by the reciprocal
x - 6 = 3 +6 +6 Numbers to other side x = 9
24) Solve: 4(x + 3) = x - 18 2 3 * 3 2 -10 * 3 2 9 -9 Answer to previous question: 24) Solve: 4(x + 3) = x - 18 Distribute first. 4x + 12 = x -18 Variables to one side -x -x 3x + 12 = -18 -12 -12 Numbers to other 3x = -30 Divide by 3 3 3 x = -10 25) How do we clear division? By adding By subtracting By multiplying |