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Mila [183]
3 years ago
9

What is are the solutions to | x+4 |= 3x-5?

Mathematics
1 answer:
bonufazy [111]3 years ago
7 0

Answer:

x = \frac{9}{2}

Step-by-step explanation:

The absolute value always returns a positive value but the expression inside can be positive or negative, that is

x + 4 = 3x - 5 ( subtract 3x from both sides )

- 2x + 4 = - 5 (subtract 4 from both sides )

- 2x = - 9 ( divide both sides by - 2 )

x = \frac{9}{2}

OR

-(x + 4) = 3x - 5

- x - 4 = 3x - 5 ( subtract 3x from both sides )

- 4x - 4 = - 5 ( add 4 to both sides )

- 4x = - 1 ( divide both sides by - 4 )

x = \frac{1}{4}

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions

| \frac{9}{2} + 4 | = | \frac{17}{2} | = \frac{17}{2}

right side = \frac{27}{2} - 5 = \frac{17}{2}

left side = right side , thus x = \frac{9}{2} is a solution

check second solution

| \frac{1}{4} + 4 | = |  \frac{17}{4} | = \frac{17}{4}

right side =   \frac{3}{4} - 5 = -   \frac{17}{4}

right side ≠ left sides, hence not a solution

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scZoUnD [109]

Answer:

a

x

2

+

b

x

+

c

=

0

the formula for the roots is

x

=

−

b

±

√

b

2

−

4

a

c

2

a

(

1

)

Identify the values for

a

,

b

,

&

c

x

2

+

4

x

+

3

=

0

cmp

a

x

2

+

b

x

+

c

=

0

a

=

1

b

=

4

c

=

3

(

2

)

Substitute these numbers into eh formula

x

=

−

4

±

√

4

2

−

(

4

×

1

×

3

)

2

×

1

(

3

)

Carefully proceed and do the calculations

x

=

−

4

±

√

16

−

12

2

x

=

−

4

±

√

4

2

x

=

−

4

±

2

2

now calculate the two separate solutions

x

1

=

−

4

+

2

2

=

−

2

2

=

−

1

x

2

=

−

4

−

2

2

=

−

6

2

=

−

3

Answer link

Step-by-step explanation:

8 0
2 years ago
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