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3 years ago

The product of two consecutive positive integers is 29 more than their sum. Find the integers

1 answer:

7 0

The consecutive positive integers would be: x and (x+1),
We would have to solve the following equation to find these numbers:
x(x+1)-[x+(x+1)]=29
x²+x-2x-1=29
x²-x-30=0
x=[1⁺₋√(1+120)]/2
x=(1⁺₋11)/2
We have two possible solutions:
x₁=(1-11)/2=-5 then: (x+1)=-5+1=-4 This is not the solution.
x₂=(1+11)/2=6 then: (x+1)=6+1=7 This solution is right.

Answer: the numbers would be 6 and 7.

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1 year ago

Help me with my math pls :)

MrMuchimi

Answer:

4(x-8)=-32+4: x=1

2(x-2)=-3-2x: x1/4

3+5x=5(x+2)-7: x=0

8x+38=-3(-6-4x) x=5

Step-by-step explanation:

4(x-8)=-32+4

add subtract the numbers

-32+4=-28

4(x-8)=-28

Divide both sides by 4

$\frac{4(x-8)}{4}=\frac{-28}{4}$

Simplify

x-8=-7

Add 8 on both sides

x+8-8=-7+8

Simplify

x=1

2(x-2)=-3-2x

Expand 2(x-2)
apply distributive law: a(b-c)=ab-ac

a=2 b=x c=2

=2x-2·2

multiply the numbers

2·2=4

=2x-4

2x-4=-3x-2

Add 4 to both sides

2x-4+4=-3-2x+4

simplify

2x=-2x+1

Add 2x on both sides

2x+2x=2x+1+2x

Simplify

4x=1

Divide by 4 on both sides

4x÷4=1÷4

Simplify

x=1/4

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

We move all terms to the left:

3+5x-(5(x+2)-7)=0

We calculate terms in parentheses: -(5(x+2)-7), so:

5(x+2)-7

We multiply parentheses

5x+10-7

We add all the numbers together, and all the variables

5x+3

Back to the equation:

-(5x+3)

We get rid of parentheses

5x-5x-3+3=0

We add all the numbers together, and all the variables

=0

x=0/1

x=0

8x+38=-3(-6-4x)

Simplifying

8x + 38 = -3(-6 + -4x)

Reorder the terms:

38 + 8x = -3(-6 + -4x)

38 + 8x = (-6 * -3 + -4x * -3)

38 + 8x = (18 + 12x)

Solving

38 + 8x = 18 + 12x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12x' to each side of the equation.

38 + 8x + -12x = 18 + 12x + -12x

Combine like terms: 8x + -12x = -4x

38 + -4x = 18 + 12x + -12x

Combine like terms: 12x + -12x = 0

38 + -4x = 18 + 0

38 + -4x = 18

Add '-38' to each side of the equation.

38 + -38 + -4x = 18 + -38

Combine like terms: 38 + -38 = 0

0 + -4x = 18 + -38

-4x = 18 + -38

Combine like terms: 18 + -38 = -20

-4x = -20

Divide each side by '-4'.

x = 5

Simplifying

x = 5

Hope this helps

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