To find the number that satisfies the equation stated in the problem, we need to set up and solve the equation step-by-step.
1. Let's define the unknown number as [tex]\( x \)[/tex].
2. According to the problem, 21 less than half the number ([tex]\( \frac{1}{2}x \)[/tex]) is the same as four times the number (4[tex]\( x \)[/tex]).
We can write this relationship as an equation:
[tex]\[ \frac{1}{2}x - 21 = 4x \][/tex]
Next, we need to solve this equation for [tex]\( x \)[/tex]:
3. First, we want to eliminate the fraction. We can do this by multiplying every term in the equation by 2 (the denominator of the fraction):
[tex]\[ 2 \left( \frac{1}{2}x \right) - 2 \cdot 21 = 2 \cdot 4x \][/tex]
This simplifies to:
[tex]\[ x - 42 = 8x \][/tex]
4. Next, we want to collect all terms involving [tex]\( x \)[/tex] on one side of the equation. To do this, let's subtract [tex]\( x \)[/tex] from both sides of the equation:
[tex]\[ x - x - 42 = 8x - x \][/tex]
Simplifying, we get:
[tex]\[ -42 = 7x \][/tex]
5. Finally, to solve for [tex]\( x \)[/tex], we divide both sides of the equation by 7:
[tex]\[ \frac{-42}{7} = \frac{7x}{7} \][/tex]
Which simplifies to:
[tex]\[ -6 = x \][/tex]
So the unknown number is [tex]\( x = -6 \)[/tex].
Therefore, the answer is:
b. -6
