Math and Arithmetic

Geometry

012

Algebraically, X = integers. X + (X + 1) = 237 gather all terms on the left 2X + 1 = 237 subtract 1 from each side 2X = 236 divide both sides integers by 2 X = 118 --------------so, X + 1 = 119 ----------------so, The two consecutive integers that = 237 are 118 and 119 -------------------

Yes. When you subtract two, you get two congruent sides.

Let x be the smallest of the consecutive odd integers. Since consecutive odd integers differ by 2, we havex + (x + 2) + (x + 4) + (x + 6) = -2204x + 12 = -220 (subtract 12 to both sides)4x = -232 (divide by 4 to both sides)x = -58Thus, the four consecutive odd integers whose sum is -220 are -58, -56, -54, and -52.

That is the correct spelling of "scalene" (in one sense a triangle with three dissimilar sides).

98 - 3x = 10x + 20, solve for x.subtract 98 from both sides-3x = 10x - 78subtract 10x from both sides-13x = -78multiply both sides by -113 x = 78divide both sides by 13x = 6

9Y + 4 = 2Y + 25 subtract 2Y from both sides 7Y + 4 = 25 subtract 4 from both sides 7Y = 21 divide both sides integers by 7 (7/7)Y = 21/7 Y = 3 -----------------check in original equation 9(3) + 4 = 2(3) + 25 27 + 4 = 6 + 25 31 = 31 ---------------checks

2x + 22 = x Subtract x from both sides: x + 22 = 0 Subtract 22 from both sides: x = -22

Let the first of the three odd consecutive integers be x, so that the second of these integers would be x + 2, and the third one would be x + 4. We have: 3x = 2[(x + 2)+ (x + 4)] + 3 3x = 2(2x + 6) +3 3x = 4x + 12 + 3 (subtract 4x to both sides) -x = 15 (multiply by -1 to both sides) x = -15 (the first one) So the integers are -15, -13, and -11. The average of those integers is (-15 + -13 + -11)/2 = -39/2 = -19.5.

Let the first one be x, the second be x + 1, and the third one is x + 2. So we have,x + x+1 + x +2 = 2283x + 3 = 228 subtract 3 to both sides3x = 225 divide by 3 to both sidesx = 75x + 1 = 75 + 1 = 76x + 2 = 75 + 2 = 77Thus, the three consecutive integers are 75, 76, and 77.

5X + 5 = 14 + 2Xsubtract 2X from both sides3X + 5 = 14subtract 5 from both sides3X = 9divide both sides integers by 3(3/3)X = 9/3X = 3=======check in original equation5(3) + 5 = 14 + 2(3)15 + 5 = 14 + 620 = 20=======checks

Well, you simply add or subtract whatever it is from both sides.Example: 5x-2=3. You subtract -2 from both sides, and you get 5x=5. This is cross-cancellation.

First you subtract 3x from both sides and get -7=2x+3. Then subtract 3 from both sides and get -10=2x. Then divide both sides by 2 and x=-5.

5x + 36 = x Subtract x from both sides: 4x + 36 = 0 Subtract 36 from both sides: 4x = -36 Divide both sides by 4: x = -9

You can add or subtract any quantity on both sides of an equation, without changing the equation's solution set. Just make sure you add or subtract the same thing on both sides.

you subtract 3 from the number of sides then multiply that by the number of sides divided by 2

70 = 81-n subtract 70 from both sides 0 = 11 - n subtract 11 from both sides -11 = -n divide both sides by -1 11 = n

There are 18, but only 7 primitive ones. The rest are similar to the primitive triangles : for example (15, 50, 25) is similar to (3, 4, 5).

3x + 4 = 2x - 3 Subtract 2x from both sides: x + 4 = - 3 Subtract 4 from both sides: x = -7

4x + 8 = 3x +1subtract 3x from both sidesx + 8 = 1subtract 8 from both sidesx = -7

3.2 + 3x = 2x - 1.4 Subtract 3.2 from both sides: 3x = 2x - 4.6 Subtract 2x from bothe sides: x = -4.6

2x + 3 = x + 1 Subtract x from both sides: x + 3 = 1 Subtract 3 from both sides: x = -2

7P + 9 = 16 + 6P subtract 6P from BOTH sides P + 9 = 16 subtract 9 from both sides P = 7

8x + 33 = 7x + 27 Subtract 7x from both sides: x + 33 = 27 Subtract 33 from both sides: x = -6

5x + 3 = 6x + 1 Subtract 5x from both sides: 3 = x + 1 Subtract 1 from both sides: 2 = x

If two rectangles are similar, they have corresponding sides and corresponding angles. Corresponding sides must have the same ratio.

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