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3 years ago

3|1/2x + 5| + 7 = 5

Mathematics

1 answer:

egoroff_w [7]3 years ago

4 0

Answer:

x is -34/3 and -26/3

Step-by-step explanation:

Given the expression

3|1/2x+5| + 7 = 5

Removing the modulus sign

3(1/2x+5) + 7 = 5

Subtract 7 from both sides

3(1/2x+5) + 7 - 7= 5 - 7

3(1/2x+5) = -2

Open the bracket

3/2 x + 15 = -2

Subtract 15 from both sides

3/2 x + 15-15 = -2 - 15

3/2 x = -17

3x = -2*17

3x = -34

x = -34/3

Hence the value of x is -34/3

For the negative function:

3(1/2x+5) + 7 = 5

Subtract 7 from both sides

3(-(1/2x+5)) + 7 - 7= 5 - 7

3(-1/2x-5) = -2

Open the bracket

-3/2 x - 15 = -2

Add 15 from both sides

3/2 x + 15-15 = -2 + 15

-3/2 x = 13

-3x = 2 * 13

-3x =26

x = -26/3

Hence the value of x is -26/3

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we are given

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to figure out $a_1$ we need to figure out the equation

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$\displaystyle \frac{ a_{1}(1 - {( \frac{1}{2} )}^{3} )}{ \dfrac{1}{2} } = 189$

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simplify substraction:

$\displaystyle \frac{ a_{1} (\frac{7}{8} )}{ \frac{1}{2} } = 189$

simplify complex fraction:

$\displaystyle a_{1} (\frac{7}{8} ) \div { \frac{1}{2} } = 189$

calculate reciprocal:

$\displaystyle a_{1} \frac{7}{8} \times 2 = 189$

reduce fraction:

$\displaystyle a_{1} \frac{7}{4} \ = 189$

multiply both sides by 4/7:

$\displaystyle a_{1} \frac{7}{4} \times \frac{4}{7} \ = 189 \times \frac{4}{7}$

reduce fraction:

$\displaystyle a_{1} = 27\times 4$

simplify multiplication:

$\displaystyle a_{1} = 108$

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