Twice a number decreased by 8 is 2 less than half the number. what is the number?

18

Step-by-step explanation:

2x - 8 = x + 10

- x       - x

x - 8 = 10

 + 8   + 8

x = 18

18

Step-by-step explanation:

set up an equation and solve

2x-8=1/2-2

Step-by-step explanation:

4

Step-by-step explanation:

with th information given we can express the equation:

[tex]2x-8=\frac{x}{2} -2[/tex]

where [tex]x[/tex] is the unknown number.

to clear for [tex]x[/tex] first we multiply the equation by 2, to eliminate the fraction:

[tex]2(2x-8=\frac{x}{2}-2 )\\4x-16=x-4[/tex]

moving all terms with [tex]x[/tex] to the left:

[tex]4x-x-16=-4\\3x-16=-4[/tex]

and adding +16 to each side:

[tex]3x-16+16=-4+16\\3x=12[/tex]

and finally, dividing by 3

[tex]x=\frac{12}{4} =4[/tex]

the number is 4.

i think the equation is

2n-8=2-1/2n

x = 4

"Translating" the sentence into numbers:

Twice a number → x * 2 or 2x

2x decreased by 8 → 2x - 8

2x - 8 is 2 less than half the number → 2x - 8 = x/2 - 2

Solving the equation:

2x - 8 = x/2 - 2

2x - 8 = 1/2x - 2

2x - 1/2x - 8 = -2

3/2x - 8 = -2

3/2x = -2 + 8

3/2x = 6

2/3x = 6 (!!)

x = 6 * 2/3

x = (6 * 2) / 3

x = 12 / 3

x = 4

(!!) → On that step what we must do is multiply both sides by 2/3 (which we obtain by flipping 3/2). But, since results would be the same, we just flipped the equation and followed a standard procedure.

Proving the equation:

2(4) - 8 = 4/2 - 2

8 - 8 = 4/2 - 2

0 = 4/2 - 2

0 = 2 - 2

0 = 0 → Both sides of the equation are equal. The equation is correct, 4 is the answer.

Hope it helped,

BiologiaMagister