Solve the equation Check the result 1 2 5x 9 Solve the eq

Solve the equation. Check the result. -1 - 2 + (5x + 9) Solve the equation. Check the result. 18 - (x + 8) = -14 x = Solve the equation and check the result. 9m - 15 - 10m + 11 m = Form an equation and solve It to answer the question. Because of increased giving, a college scholarship program awarded four more scholarships this year than last year. If a total of 44 scholarships were awarded over the last two years, how many were awarded last year and how many were awarded this year? Form an equation and solve it to answer the question. The perimeter of a rectangle is 90 Inches. Find the length and the width if the length is two times the width. Form an equation and solve it to answer the question. Four less than four times a number is the same as the number increased by eleven. What is the number?

Solution

-1 = 2 + 3(5x + 9)
-1 = 2 + 15x + 27
-1 = 15x + 29
-1 - 29 = 15x
15x = -30
x = -30/15
x = -2

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18 - (x + 8) = -14
18 - x - 8 = -14
10 - x = -14
-x = -14 - 10
-x = -24
x = 24

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9m - 15 = 10m + 11
9m - 10m - 15 = 11
-m - 15 = 11
-m = 11 + 15
-m = 26
Thus m = -26

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Last year, say x scholarships
This yr, say (x + 4) scholships

Adding them :
x + x + 4 = 44
2x + 4 = 44
2x = 40
x = 20

Last yr : 20
This yr : 24

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L = 2x
Width = x

So, P = 2(L + B)

90 = 2(2x+ x)

6x = 90

x = 15

Thus, length = 30
width = 15

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4 times a number is 4x
4 less than 4 times a number is : 4x - 4

Num increased by 11 : x + 11

These are equal

4x - 4 = x + 11

4x - x = 11 + 4

3x = 15

x = 5

So, the number is 5