Evaluate the expression 1 2/3 - 1 2/3 x 1/4 and solve the equation 5x - 8 - 3(x + 1) = -7.

Welcome back Jedidah🎀 — been a while! Let's pick up where you left off. a) To evaluate the expression, we first convert the mixed numbers to improper fractions and follow the order of operations (multiplication before subtraction). Step 1: Convert mixed numbers to improper fractions and perform multiplication. 1(2)/(3) - 1(2)/(3) × (1)/(4) = (5)/(3) - (5)/(3) × (1)/(4) = (5)/(3) - (5 × 1)/(3 × 4) = (5)/(3) - (5)/(12) Step 2: Find a common denominator and subtract the fractions. The common denominator for 3 and 12 is 12. = (5 × 4)/(3 × 4) - (5)/(12) = (20)/(12) - (5)/(12) = (20 - 5)/(12) = (15)/(12) Step 3: Simplify the fraction. = (5)/(4) = 1(1)/(4) The final answer is 1(1)/(4) or 1.25. b) To solve the equation, we first expand the parenthesis and then combine like terms to isolate x. Step 1: Distribute the -3 into the parenthesis. 5x - 8 - 3(x + 1) = -7 5x - 8 - 3x - 3 = -7 Step 2: Combine like terms on the left side. (5x - 3x) + (-8 - 3) = -7 2x - 11 = -7 Step 3: Add 11 to both sides of the equation. 2x - 11 + 11 = -7 + 11 2x = 4 Step 4: Divide both sides by 2. (2x)/(2) = (4)/(2) x = 2 The final answer is x = 2. c) To simplify the expression, we expand the parenthesis and then combine like terms. Step 1: Distribute 5 into the first parenthesis and -2 into the second parenthesis. 5(2y - 3) - 2(5 - 2y) = (5 × 2y) + (5 × -3) + (-2 × 5) + (-2 × -2y) = 10y - 15 - 10 + 4y Step 2: Combine like terms. (10y + 4y) + (-15 - 10) = 14y - 25 The final answer is 14y - 25. d) To calculate the number of unused units, we first find the amount of memory used and then subtract it from the total capacity. Step 1: Calculate the amount of memory used. Total capacity = 512 units. Fraction used = (2)/(3). Memory used = (2)/(3) × 512 units = (1024)/(3) units = 341.333... units Step 2: Calculate the number of unused units. Unused units = Total capacity - Memory used = 512 - (1024)/(3) = (512 × 3)/(3) - (1024)/(3) = (1536)/(3) - (1024)/(3) = (1536 - 1024)/(3) = (512)/(3) units Step 3: Convert to a decimal and round to 2 decimal places. = 170.666... units Rounding to 2 decimal places, we get 170.67 units. The final answer is 170.67 units. Drop the next question! 📸