Final answer:
The sentence 'Ten more than half of a number is twenty-two' translates into the algebraic equation 0.5x + 10 = 22. After simplifying by multiplying both sides by 2, it becomes x + 20 = 44. This can now be solved to find the value of the number x.
Step-by-step explanation:
The sentence "Ten more than half of a number is twenty-two" can be translated into the algebraic equation by expressing each part of the sentence as a mathematical statement. "Half of a number" suggests that we divide the number (let's represent it with 'x') by 2, which is written as 0.5x or x/2. "Ten more than" tells us to add 10 to that half, and "is twenty-two" gives us the total which the expression should equal. Therefore, the equation would be 0.5x + 10 = 22.
Now we proceed to simplify the equation. As guided in Step 4, we begin by eliminating the fractional coefficient by multiplying both sides of the equation by 2. This step would transform the equation to:
2 x (0.5x + 10) = 2 x 22
Which simplifies to:
1 x x + 20 = 44
And further simplifies to:
x + 20 = 44.
Now we have a simple equation to solve where the variable x is the number we are looking for.