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Solving Equations
Number of Solutions:
0, 1, or Infinity
Absolute Value Equations
Literal Equations
Word Problems
100
4(x+3) - 2x = 16
x = 2
100
3x + 7 = 2x + (x + 6)
7=6 => NO SOLUTION
100
| x+8| = 2
x = -6 OR x = -10 (NEED BOTH)
100
Solve for x. y = 3x + 1
x = ( y-1 ) / 3
100
WRITE AN EQUATION & SOLVE: Rob drives for 2 1/2 hours, traveling 160 miles total. What is his average speed?
x - Rob's average speed. ~ d = rt ~ 160 = x (2.5) ~ x = 64 ~ Rob's average speed is 64 MPH.
200
3x - (x+7) = -9
x = -1
200
6x + 8 = 4(x+2)
x = 0 => ONE SOLUTION
200
| 2x+1 | = 3
x = 1 OR x = -2 (NEED BOTH)
200
Solve for h. V = lwh
h = V / (lw)
200
WRITE AN EQUATION & SOLVE: Sally buys t-shirts for her Relay for Life team. She has to pay $5 for a setup fee and then pays $8 per shirt. How many shirts did she order if it costs $93?
x - number of shirts ~ 5 + 8x = 93 ~ x = 11 ~ Sally buys 11 shirts.
300
2x + 6 = 5x - 15
x = 7
300
3x - (8-2x) = -8 + 5x
-8 = -8 => INFINITELY MANY SOLUTIONS
300
| 4x+5 | = -10
Absolute Value cannot equal a negative => NO SOLUTION
300
Solve for w. 6P = 12d + 2w
w = 3P - 6d
300
WRITE AN EQUATION & SOLVE: Three consecutive even integers have a sum of 18. Find the integers.
x - First Even Integer ~ x+2 - Next Even Integer ~ x+4 - Third Even Integer ~ x + (x+2) + (x+4) = 18 ~ x = 4 ~ The three integers are 4, 6, and 8.
400
2(x-5) - 4(x-2) = 3 - 3x
x = 5
400
3(2x+6) = 2(2x-7) + 24
x = -4 => ONE SOLUTION
400
| x-5 | - 3 = -2
x = 6 OR x = 4 (NEED BOTH)
400
Solve for x. y = 3x + xz
x = y / (3+z)
400
WRITE AN EQUATION & SOLVE: Find four consecutive integers such that the sum of the first two is 15 less than triple the largest.
x - first integer ~ x+1 - second integer ~ x+2 - third integer ~ x+3 - fourth integer ~ x + (x+1) = 3(x+3) - 15 ~ x = 7 ~ The integers are 7, 8, 9, and 10.
500
4x + 7 = 8(x-1) + 1
x = 7/2 or 3 1/2 or 3.5
500
4(x+7) - 3(2-x) = 5(x+3) + 2(5+x)
22 = 25 => NO SOLUTION
500
3 | 2x+3 | + 7 = 13
x = -1/2 OR x = -5/2 (NEED BOTH)
500
Solve for y. 5x + y = 2 - xy
y = (2-5x) / (1+x)
500
WRITE AN EQUATION & SOLVE: The width of a rectangle is 1/2 of it length. Its perimeter is 21 inches. Find its dimensions.
x - length ~ 1/2 x - width ~ x + 1/2 x + x + 1/2 x = 21 ~ x = 7 ~ The rectangle is 7 inches x 3.5 inches.