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3 years ago

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Mathematics

1 answer:

liraira [26]3 years ago

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1. 4(2+3c) = 56

c = 4

3. -29 = 5(2a-1)+2a

a = -2

5 . 7p-(3p+4) = -2(2p-1)+10

p=2

7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)

x=4

Step-by-step explanation:

1. 4(2+3c) = 56

$4(2+3c) = 56\\8+12c = 56$

Subtracting 8 from both sides

$8-8+12c = 56-8\\12c = 48$

Dividing both sides by 12

$\frac{12c}{12} = \frac{48}{12}\\c = 4$

Checking:

$4[2+3(4)] = 56\\4(2+12) = 56\\4(14) = 56\\56 = 56$

3. -29 = 5(2a-1)+2a

Simplifying

$-29 = 10a-5+2a\\-29 = 12a-5$

Adding 5 on both sides

$-29+5 = 12a - 5+5\\-24 = 12a$

Dividing both sides by 12

$\frac{12a}{12} = \frac{-24}{12}\\a = -2$

Checking:

$-29 = 5(2a-1)+2a\\-29 = 5[2(-2)-1]+2(-2)\\-29 = 5(-4-1) -4\\-29 = 5(-5) -4\\-29 = -25-4\\-29 = -29$

5 . 7p-(3p+4) = -2(2p-1)+10

Simplifying

$7p-3p-4 = -4p+2+10\\4p-4 = -4p+12$

Adding 4 on both sides

$4p-4+4 = -4p+12+4\\4p = -4p+16$

Adding 4p on both sides

$4p+4p = -4p+4p+16\\8p = 16$

Dividing both sides by 8

$\frac{8p}{8} = \frac{16}{8}\\p = 2$

Checking:

$7p-(3p+4) = -2(2p-1)+10\\7(2)-[3(2)+4] = -2[2(2)-1] +10\\14 - (6+4) = -2 (4-1) +10\\14 - 10 = -2(3) +10\\4 = -6+10\\4=4$

7. 1/2 (-4+6x) = 1/3x + 2/3*(x+9)

Simplifying

$\frac{1}{2} (-4+6x) = \frac{1}{3}x+\frac{2}{3}(x+9)\\\frac{-4}{2}+\frac{6x}{2} = \frac{x}{3} +\frac{2x}{3} + \frac{18}{3}\\-2+3x = \frac{x+2x+18}{3}\\-2+3x = \frac{3x+18}{3}\\3(-2+3x) = 3x+18\\-6+9x = 3x+18$

Adding 6 on both sides

$-6+6+9x = 3x+18+6\\9x = 3x+24$

Subtracting 3x from both sides

$9x-3x = 3x-3x+24\\6x = 24$

Dividing both sides by 6

$\frac{6x}{6} = \frac{24}{6}\\x = 4$

Checking:

$\frac{1}{2} [-4+6(4)] = \frac{1}{3}(4)+\frac{2}{3}(4+9)\\\frac{1}{2}(-4+24) = \frac{4}{3}+\frac{2}{3}(13)\\\frac{1}{2}(20) = \frac{4}{3} +\frac{26}{3}\\15 = \frac{4+26}{3}\\15 = \frac{30}{3}\\15=15$