Algebraic expression: 4x + 2 Algebraic equation: 4x + 2 = 100
3x2 + 5 + 4x3 - x2 + 2x3 + 9 = 3x2 - x2 + 4x3 + 2x3 + 5 + 9 = 2x2 + 6x3 + 14
3x + 15 = 9x + 30 You can see that each coefficient can be divisible by 3. Just “factor out” the number 3 by dividing each term by 3 to get your simplified equation. 3x/3 + 15/3 = 9x/3 + 30/3 = x + 5 = 3x + 10
(3 + 5)2 x 10 + 4 First, follow P, the operation in the parentheses: = (8)2 x 10 + 4 Then, follow E, the operation of the exponent: = 64 x 10 + 4 Next, do multiplication: = 640 + 4 And last, do addition: = 644
5x + 15 = 65 = 5x/5 + 15/5 = 65/5 = x + 3 = 13 = x = 10
4x + 16 = 25 -3x = 4x = 25 -16 - 3x 4x + 3x = 25 -16 = 7x = 9 7x/7 = 9/7 = x = 9/7
2x2 + 12 = 44 First, subtract 12 from both sides. 2x2 + 12 -12 = 44 -12 = 2x2 = 32 Next, divide both sides by 2. 2x2/2 = 32/2 = x2 = 16 Solve by taking the square root of both sides, since that will turn x2 into x. √x2 = √16 = State both answers:x = 4, -4
(x + 3)/6 = 2/3 First, cross multiply to get rid of the fraction. You have to multiply the numerator of one fraction by the denominator of the other. (x + 3) x 3 = 2 x 6 = 3x + 9 = 12 Now, combine like terms. Combine the constant terms, 9 and 12, by subtracting 9 from both sides. 3x + 9 - 9 = 12 - 9 = 3x = 3 Isolate the variable, x, by dividing both sides by 3 and you’ve got your answer. 3x/3 = 3/3 = x =1
√(2x+9) - 5 = 0 First, move everything that isn’t under the radical sign to the other side of the equation: √(2x+9) = 5 Then, square both sides to remove the radical: (√(2x+9))2 = 52 = 2x + 9 = 25 Now, solve the equation as you normally would by combining the constants and isolating the variable: 2x = 25 - 9 = 2x = 16 x = 8
Here’s how you solve for the absolute value by isolating the absolute value and then removing it: |4x +2| - 6 = 8 = |4x +2| = 8 + 6 = |4x +2| = 14 = 4x + 2 = 14 = 4x = 12 x = 3 Now, solve again by flipping the sign of the term on the other side of the equation after you’ve isolated the absolute value: |4x +2| = 14 = 4x + 2 = -14 4x = -14 -2 4x = -16 4x/4 = -16/4 = x = -4 Now, just state both answers: x = -4, 3
