Mathematics, 17.06.2020 09:57 gabriellaalvarez84

7x + 2 = -19 (b) 3x - 1/3 = 5 (c) 5x - 4 = 21 (d) -7x = 21 (e) 18 - 7x = -3 (f) 3(x + 4) = 21 (g) 3x - 9 = 5x - 3 (h) 4x + 6 - 7x + 9 = 18 (i) - 4/9 x = - 36 (j) -7/8x - 6 = 8 can any please elp me find the variables in the question

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Answer from: akatherine1738

Step-by-step explanation:

a)7x + 2 = -19 {subtract 2 from both sides}

7x + 2 - 2 = -19 - 2

7x = -21 {Divide both sides by 7}

7x/7 = -21/7

x = -3

b) 3x - 1/3 = 5

3x - 1/3 +1/3 = 5 + 1/3 {Add 1/3 to both sides}

3x =15/3 + 1/3

3x =16/3

3x/3 = 16/3*3 {Divide both sides by 3}

x =16/9

x =1 7/9

c) 5x - 4 = 21

5x -4 + 4 = 21 +4 {Add 4 to both sides}

5x = 25

5x/5 = 25/5 {Divide both sides by 5}

x = 5

d) -7x = 21 {Divide both sides by -7}

-7x/-7 = 21/-7

x = -3

e) 18 - 7x = -3

18 - 7x - 18 = -3 - 18 {Subtract 18 from both sides}

-7x = -21 {Divide both sides by -7}

-7x/-7 = -21/-7

x = 3

f) 3(x+4) = 21 {use distributive property}

3x + 3*4 = 21

3x + 12 = 21

3x + 12 - 12 = 21 - 12 {Subtract 12 from both sides}

3x = 9 {Divide both sides by 3}

3x/3 = 9/3

x = 3

g) 3x - 9 = 5x - 3 {add 9 to both sides}

3x - 9 + 9 = 5x - 3 + 9

3x = 5x + 6

3x - 5x = 5x + 6 - 5x { subtract 5x form both sides}

-2x = 6 {Divide both sides by -2}

-2x/-2 = 6/-2

x = -3

h) 4x + 6 - 7x + 9 = 18 {Add the like terms}

-3x + 15 = 18 {Subtract 15 from both sides}

-3x + 15 -15 = 18 - 15

-3x = 3 {Divide both sides by -3}

-3x/-3 = 3/-3

x = -1

$i) \frac{-4}{9}x = -36$

Multiply both sides by 9

$9*\frac{-4}{9}x =9*-36$

-4x = -324 {Divide both sides by -4}

-4x/-4 = -324/-4

x = -81

$j)\frac{-7}{8}x - 6 = 8$ {Add 6 to both sides}

$\frac{-7}{8}x-6+6=8+6\\\\\frac{-7}{8}x=14\\$ {Multiply both sides by 8}

$\frac{-7}{8}x*8=14*8\\\\-7x=14*8\\$ {Divide both sides by -7}

$\frac{-7}{-7}x=\frac{14*8}{-7}$

x =-2*8

x = -16

Answer from: Quest

$2^{2x+11}=3^{x-31}$

take the logarithm of both sides (the base of the log doesn't matter):

$\ln2^{2x+11}=\ln3^{x-31}$

apply the exponent property - this says that $\ln a^b=b\ln a$ :

$(2x+11)\ln2=(x-31)\ln3$

distribute the log terms on both sides:

$(2\ln2)x+11\ln2=(\ln3)x-31\ln3$

group like terms together:

$(2\ln2-\ln3)x=-11\ln2-31\ln3$

divide through both sides by the coefficient on $x$ :

$x=-\dfrac{11\ln2+31\ln3}{2\ln2-\ln3}$

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

$x=-\dfrac{\ln2^{11}+\ln3^{31}}{\ln2^2-\ln3}$

$x=-\dfrac{\ln2^{11}3^{31}}{\ln\frac43}$

$x=-\log_{4/3}2^{11}3^{31}$

Answer from: Quest

answer is 1

step-by-step explanation:

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7x + 2 = -19 (b) 3x - 1/3 = 5 (c) 5x - 4 = 21 (d) -7x = 21 (e) 18 - 7x = -3 (f) 3(x + 4) = 21 (g) 3x...

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