Here are the solutions to your problems: Problem 1: Simplify the expression Step 1: Combine the terms with $x$. $$5x + 10x - 2x + 4 = (5 + 10 - 2)x + 4$$ Step 2: Perform the arithmetic within the parentheses. $$(5 + 10 - 2)x + 4 = (15 - 2)x + 4$$ $$= 13x + 4$$ The simplified expression is: $$\boxed{13x + 4}$$ Problem 2: Convert 21 from base 10 to base 2 Step 1: Divide 21 by 2 and record the remainder. $$21 \div 2 = 10 \text{ remainder } 1$$ Step 2: Divide the quotient (10) by 2 and record the remainder. $$10 \div 2 = 5 \text{ remainder } 0$$ Step 3: Divide the quotient (5) by 2 and record the remainder. $$5 \div 2 = 2 \text{ remainder } 1$$ Step 4: Divide the quotient (2) by 2 and record the remainder. $$2 \div 2 = 1 \text{ remainder } 0$$ Step 5: Divide the quotient (1) by 2 and record the remainder. $$1 \div 2 = 0 \text{ remainder } 1$$ Step 6: Read the remainders from bottom to top to get the base 2 number. The remainders are $1, 0, 1, 0, 1$. So, $21_{10}$ in base 2 is: $$\boxed{10101_2}$$ Problem 3: Solve $12.5 \times 0.4$ without using a calculator Step 1: Multiply the numbers as if they were whole numbers, ignoring the decimal points for now. $$125 \times 4$$ Step 2: Perform the multiplication. $$125 \times 4 = 500$$ Step 3: Count the total number of decimal places in the original numbers. $12.5$ has one decimal place. $0.4$ has one decimal place. Total decimal places = $1 + 1 = 2$. Step 4: Place the decimal point in the product (500) two places from the right. $$5.00$$ $$5.00 = 5$$ The product is: $$\boxed{5}$$